--- /dev/null
+# Created by Octave 3.6.1, Sun May 13 12:55:35 2012 UTC <root@brouzouf>
+# name: cache
+# type: cell
+# rows: 3
+# columns: 77
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 20
+anderson_darling_cdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2184
+ -- Function File: P = anderson_darling_cdf (A, N)
+ Return the CDF for the given Anderson-Darling coefficient A
+ computed from N values sampled from a distribution. For a vector
+ of random variables X of length N, compute the CDF of the values
+ from the distribution from which they are drawn. You can uses
+ these values to compute A as follows:
+
+ A = -N - sum( (2*i-1) .* (log(X) + log(1 - X(N:-1:1,:))) )/N;
+
+ From the value A, `anderson_darling_cdf' returns the probability
+ that A could be returned from a set of samples.
+
+ The algorithm given in [1] claims to be an approximation for the
+ Anderson-Darling CDF accurate to 6 decimal points.
+
+ Demonstrate using:
+
+ n = 300; reps = 10000;
+ z = randn(n, reps);
+ x = sort ((1 + erf (z/sqrt (2)))/2);
+ i = [1:n]' * ones (1, size (x, 2));
+ A = -n - sum ((2*i-1) .* (log (x) + log (1 - x (n:-1:1, :))))/n;
+ p = anderson_darling_cdf (A, n);
+ hist (100 * p, [1:100] - 0.5);
+
+ You will see that the histogram is basically flat, which is to say
+ that the probabilities returned by the Anderson-Darling CDF are
+ distributed uniformly.
+
+ You can easily determine the extreme values of P:
+
+ [junk, idx] = sort (p);
+
+ The histograms of various P aren't very informative:
+
+ histfit (z (:, idx (1)), linspace (-3, 3, 15));
+ histfit (z (:, idx (end/2)), linspace (-3, 3, 15));
+ histfit (z (:, idx (end)), linspace (-3, 3, 15));
+
+ More telling is the qqplot:
+
+ qqplot (z (:, idx (1))); hold on; plot ([-3, 3], [-3, 3], ';;'); hold off;
+ qqplot (z (:, idx (end/2))); hold on; plot ([-3, 3], [-3, 3], ';;'); hold off;
+ qqplot (z (:, idx (end))); hold on; plot ([-3, 3], [-3, 3], ';;'); hold off;
+
+ Try a similarly analysis for Z uniform:
+
+ z = rand (n, reps); x = sort(z);
+
+ and for Z exponential:
+
+ z = rande (n, reps); x = sort (1 - exp (-z));
+
+ [1] Marsaglia, G; Marsaglia JCW; (2004) "Evaluating the Anderson
+ Darling distribution", Journal of Statistical Software, 9(2).
+
+ See also: anderson_darling_test
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Return the CDF for the given Anderson-Darling coefficient A computed
+from N valu
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 21
+anderson_darling_test
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1834
+ -- Function File: [Q, ASQ, INFO] = = anderson_darling_test (X,
+ DISTRIBUTION)
+ Test the hypothesis that X is selected from the given distribution
+ using the Anderson-Darling test. If the returned Q is small,
+ reject the hypothesis at the Q*100% level.
+
+ The Anderson-Darling A^2 statistic is calculated as follows:
+
+ n
+ A^2_n = -n - SUM (2i-1)/n log(z_i (1 - z_{n-i+1}))
+ i=1
+
+ where z_i is the ordered position of the X's in the CDF of the
+ distribution. Unlike the Kolmogorov-Smirnov statistic, the
+ Anderson-Darling statistic is sensitive to the tails of the
+ distribution.
+
+ The DISTRIBUTION argument must be a either "uniform", "normal", or
+ "exponential".
+
+ For "normal"' and "exponential" distributions, estimate the
+ distribution parameters from the data, convert the values to CDF
+ values, and compare the result to tabluated critical values. This
+ includes an correction for small N which works well enough for N
+ >= 8, but less so from smaller N. The returned
+ `info.Asq_corrected' contains the adjusted statistic.
+
+ For "uniform", assume the values are uniformly distributed in
+ (0,1), compute A^2 and return the corresponding p-value from
+ `1-anderson_darling_cdf(A^2,n)'.
+
+ If you are selecting from a known distribution, convert your
+ values into CDF values for the distribution and use "uniform". Do
+ not use "uniform" if the distribution parameters are estimated
+ from the data itself, as this sharply biases the A^2 statistic
+ toward smaller values.
+
+ [1] Stephens, MA; (1986), "Tests based on EDF statistics", in
+ D'Agostino, RB; Stephens, MA; (eds.) Goodness-of-fit Techinques.
+ New York: Dekker.
+
+ See also: anderson_darling_cdf
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Test the hypothesis that X is selected from the given distribution
+using the And
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+anovan
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1504
+ -- Function File: [PVAL, F, DF_B, DF_E] = anovan (DATA, GRPS)
+ -- Function File: [PVAL, F, DF_B, DF_E] = anovan (DATA, GRPS,
+ 'param1', VALUE1)
+ Perform a multi-way analysis of variance (ANOVA). The goal is to
+ test whether the population means of data taken from K different
+ groups are all equal.
+
+ Data is a single vector DATA with groups specified by a
+ corresponding matrix of group labels GRPS, where GRPS has the same
+ number of rows as DATA. For example, if DATA = [1.1;1.2]; GRPS=
+ [1,2,1; 1,5,2]; then data point 1.1 was measured under conditions
+ 1,2,1 and data point 1.2 was measured under conditions 1,5,2.
+ Note that groups do not need to be sequentially numbered.
+
+ By default, a 'linear' model is used, computing the N main effects
+ with no interactions. this may be modified by param 'model'
+
+ p= anovan(data,groups, 'model', modeltype) - modeltype = 'linear':
+ compute N main effects - modeltype = 'interaction': compute N
+ effects and N*(N-1) two-factor
+ interactions - modeltype = 'full': compute interactions at all
+ levels
+
+ Under the null of constant means, the statistic F follows an F
+ distribution with DF_B and DF_E degrees of freedom.
+
+ The p-value (1 minus the CDF of this distribution at F) is
+ returned in PVAL.
+
+ If no output argument is given, the standard one-way ANOVA table is
+ printed.
+
+ BUG: DFE is incorrect for modeltypes != full
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 49
+Perform a multi-way analysis of variance (ANOVA).
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+betastat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 993
+ -- Function File: [M, V] = betastat (A, B)
+ Compute mean and variance of the beta distribution.
+
+Arguments
+---------
+
+ * A is the first parameter of the beta distribution. A must be
+ positive
+
+ * B is the second parameter of the beta distribution. B must be
+ positive
+ A and B must be of common size or one of them must be scalar
+
+Return values
+-------------
+
+ * M is the mean of the beta distribution
+
+ * V is the variance of the beta distribution
+
+Examples
+--------
+
+ a = 1:6;
+ b = 1:0.2:2;
+ [m, v] = betastat (a, b)
+
+ [m, v] = betastat (a, 1.5)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 51
+Compute mean and variance of the beta distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+binostat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1057
+ -- Function File: [M, V] = binostat (N, P)
+ Compute mean and variance of the binomial distribution.
+
+Arguments
+---------
+
+ * N is the first parameter of the binomial distribution. The
+ elements of N must be natural numbers
+
+ * P is the second parameter of the binomial distribution. The
+ elements of P must be probabilities
+ N and P must be of common size or one of them must be scalar
+
+Return values
+-------------
+
+ * M is the mean of the binomial distribution
+
+ * V is the variance of the binomial distribution
+
+Examples
+--------
+
+ n = 1:6;
+ p = 0:0.2:1;
+ [m, v] = binostat (n, p)
+
+ [m, v] = binostat (n, 0.5)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 55
+Compute mean and variance of the binomial distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+boxplot
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2363
+ -- Function File: S = boxplot (DATA, NOTCHED, SYMBOL, VERTICAL,
+ MAXWHISKER, ...)
+ -- Function File: [... H]= boxplot (...)
+ Produce a box plot.
+
+ The box plot is a graphical display that simultaneously describes
+ several important features of a data set, such as center, spread,
+ departure from symmetry, and identification of observations that
+ lie unusually far from the bulk of the data.
+
+ DATA is a matrix with one column for each data set, or data is a
+ cell vector with one cell for each data set.
+
+ NOTCHED = 1 produces a notched-box plot. Notches represent a robust
+ estimate of the uncertainty about the median.
+
+ NOTCHED = 0 (default) produces a rectangular box plot.
+
+ NOTCHED in (0,1) produces a notch of the specified depth. notched
+ values outside (0,1) are amusing if not exactly practical.
+
+ SYMBOL sets the symbol for the outlier values, default symbol for
+ points that lie outside 3 times the interquartile range is 'o',
+ default symbol for points between 1.5 and 3 times the interquartile
+ range is '+'.
+
+ SYMBOL = '.' points between 1.5 and 3 times the IQR is marked with
+ '.' and points outside 3 times IQR with 'o'.
+
+ SYMBOL = ['x','*'] points between 1.5 and 3 times the IQR is
+ marked with 'x' and points outside 3 times IQR with '*'.
+
+ VERTICAL = 0 makes the boxes horizontal, by default VERTICAL = 1.
+
+ MAXWHISKER defines the length of the whiskers as a function of the
+ IQR (default = 1.5). If MAXWHISKER = 0 then `boxplot' displays all
+ data values outside the box using the plotting symbol for points
+ that lie outside 3 times the IQR.
+
+ Supplemental arguments are concatenated and passed to plot.
+
+ The returned matrix S has one column for each data set as follows:
+
+ 1 Minimum
+ 2 1st quartile
+ 3 2nd quartile (median)
+ 4 3rd quartile
+ 5 Maximum
+ 6 Lower confidence limit for median
+ 7 Upper confidence limit for median
+
+ The returned structure H has hanldes to the plot elements, allowing
+ customization of the visualization using set/get functions.
+
+ Example
+
+ title ("Grade 3 heights");
+ axis ([0,3]);
+ tics ("x", 1:2, {"girls"; "boys"});
+ boxplot ({randn(10,1)*5+140, randn(13,1)*8+135});
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 19
+Produce a box plot.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+caseread
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 264
+ -- Function File: NAMES = caseread (FILENAME)
+ Read case names from an ascii file.
+
+ Essentially, this reads all lines from a file as text and returns
+ them in a string matrix.
+
+ See also: casewrite, tblread, tblwrite, csv2cell, cell2csv, fopen
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 35
+Read case names from an ascii file.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 9
+casewrite
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 257
+ -- Function File: casewrite (STRMAT, FILENAME)
+ Write case names to an ascii file.
+
+ Essentially, this writes all lines from STRMAT to FILENAME (after
+ deblanking them).
+
+ See also: caseread, tblread, tblwrite, csv2cell, cell2csv, fopen
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 34
+Write case names to an ascii file.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+chi2stat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 800
+ -- Function File: [M, V] = chi2stat (N)
+ Compute mean and variance of the chi-square distribution.
+
+Arguments
+---------
+
+ * N is the parameter of the chi-square distribution. The
+ elements of N must be positive
+
+Return values
+-------------
+
+ * M is the mean of the chi-square distribution
+
+ * V is the variance of the chi-square distribution
+
+Example
+-------
+
+ n = 1:6;
+ [m, v] = chi2stat (n)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 57
+Compute mean and variance of the chi-square distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 11
+cl_multinom
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2978
+ -- Function File: CL = cl_multinom (X, N, B, CALCULATION_TYPE ) -
+ Confidence level of multinomial portions
+ Returns confidence level of multinomial parameters estimated p =
+ x / sum(x) with predefined confidence interval B. Finite
+ population is also considered.
+
+ This function calculates the level of confidence at which the
+ samples represent the true distribution given that there is a
+ predefined tolerance (confidence interval). This is the upside
+ down case of the typical excercises at which we want to get the
+ confidence interval given the confidence level (and the estimated
+ parameters of the underlying distribution). But once we accept
+ (lets say at elections) that we have a standard predefined maximal
+ acceptable error rate (e.g. B=0.02 ) in the estimation and we just
+ want to know that how sure we can be that the measured proportions
+ are the same as in the entire population (ie. the expected value
+ and mean of the samples are roghly the same) we need to use this
+ function.
+
+Arguments
+---------
+
+ * X : int vector : sample frequencies bins
+
+ * N : int : Population size that was sampled by x. If
+ N<sum(x), infinite number assumed
+
+ * B : real, vector : confidence interval if
+ vector, it should be the size of x containing confence
+ interval for each cells if scalar, each cell will
+ have the same value of b unless it is zero or -1
+ if value is 0, b=.02 is assumed which is standard choice at
+ elections otherwise it is calculated in a way that
+ one sample in a cell alteration defines the confidence
+ interval
+
+ * CALCULATION_TYPE : string : (Optional), described below
+ "bromaghin" (default) - do not change it unless
+ you have a good reason to do so "cochran"
+ "agresti_cull" this is not exactly the solution at reference
+ given below but an adjustment of the solutions above
+
+Returns
+-------
+
+ Confidence level.
+
+Example
+-------
+
+ CL = cl_multinom( [27;43;19;11], 10000, 0.05 ) returns 0.69
+confidence level.
+
+References
+----------
+
+ "bromaghin" calculation type (default) is based on is based on the
+article Jeffrey F. Bromaghin, "Sample Size Determination for Interval
+Estimation of Multinomial Probabilities", The American Statistician
+vol 47, 1993, pp 203-206.
+
+ "cochran" calculation type is based on article Robert T.
+Tortora, "A Note on Sample Size Estimation for Multinomial
+Populations", The American Statistician, , Vol 32. 1978, pp 100-102.
+
+ "agresti_cull" calculation type is based on article in which
+Quesenberry Hurst and Goodman result is combined A. Agresti and B.A.
+Coull, "Approximate is better than \"exact\" for interval estimation of
+binomial portions", The American Statistician, Vol. 52, 1998, pp 119-126
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Returns confidence level of multinomial parameters estimated p = x /
+sum(x) wi
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+combnk
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 93
+ -- Function File: C = combnk (DATA, K)
+ Return all combinations of K elements in DATA.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 46
+Return all combinations of K elements in DATA.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 9
+copulacdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2148
+ -- Function File: P = copulacdf (FAMILY, X, THETA)
+ -- Function File: copulacdf ('t', X, THETA, NU)
+ Compute the cumulative distribution function of a copula family.
+
+Arguments
+---------
+
+ * FAMILY is the copula family name. Currently, FAMILY can be
+ `'Gaussian'' for the Gaussian family, `'t'' for the Student's
+ t family, `'Clayton'' for the Clayton family, `'Gumbel'' for
+ the Gumbel-Hougaard family, `'Frank'' for the Frank family,
+ `'AMH'' for the Ali-Mikhail-Haq family, or `'FGM'' for the
+ Farlie-Gumbel-Morgenstern family.
+
+ * X is the support where each row corresponds to an observation.
+
+ * THETA is the parameter of the copula. For the Gaussian and
+ Student's t copula, THETA must be a correlation matrix. For
+ bivariate copulas THETA can also be a correlation coefficient.
+ For the Clayton family, the Gumbel-Hougaard family, the Frank
+ family, and the Ali-Mikhail-Haq family, THETA must be a
+ vector with the same number of elements as observations in X
+ or be scalar. For the Farlie-Gumbel-Morgenstern family, THETA
+ must be a matrix of coefficients for the
+ Farlie-Gumbel-Morgenstern polynomial where each row
+ corresponds to one set of coefficients for an observation in
+ X. A single row is expanded. The coefficients are in binary
+ order.
+
+ * NU is the degrees of freedom for the Student's t family. NU
+ must be a vector with the same number of elements as
+ observations in X or be scalar.
+
+Return values
+-------------
+
+ * P is the cumulative distribution of the copula at each row of
+ X and corresponding parameter THETA.
+
+Examples
+--------
+
+ x = [0.2:0.2:0.6; 0.2:0.2:0.6];
+ theta = [1; 2];
+ p = copulacdf ("Clayton", x, theta)
+
+ x = [0.2:0.2:0.6; 0.2:0.1:0.4];
+ theta = [0.2, 0.1, 0.1, 0.05];
+ p = copulacdf ("FGM", x, theta)
+
+References
+----------
+
+ 1. Roger B. Nelsen. `An Introduction to Copulas'. Springer, New
+ York, second edition, 2006.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 64
+Compute the cumulative distribution function of a copula family.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 9
+copulapdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1451
+ -- Function File: P = copulapdf (FAMILY, X, THETA)
+ Compute the probability density function of a copula family.
+
+Arguments
+---------
+
+ * FAMILY is the copula family name. Currently, FAMILY can be
+ `'Clayton'' for the Clayton family, `'Gumbel'' for the
+ Gumbel-Hougaard family, `'Frank'' for the Frank family, or
+ `'AMH'' for the Ali-Mikhail-Haq family.
+
+ * X is the support where each row corresponds to an observation.
+
+ * THETA is the parameter of the copula. The elements of THETA
+ must be greater than or equal to `-1' for the Clayton family,
+ greater than or equal to `1' for the Gumbel-Hougaard family,
+ arbitrary for the Frank family, and greater than or equal to
+ `-1' and lower than `1' for the Ali-Mikhail-Haq family.
+ Moreover, THETA must be non-negative for dimensions greater
+ than `2'. THETA must be a column vector with the same number
+ of rows as X or be scalar.
+
+Return values
+-------------
+
+ * P is the probability density of the copula at each row of X
+ and corresponding parameter THETA.
+
+Examples
+--------
+
+ x = [0.2:0.2:0.6; 0.2:0.2:0.6];
+ theta = [1; 2];
+ p = copulapdf ("Clayton", x, theta)
+
+ p = copulapdf ("Gumbel", x, 2)
+
+References
+----------
+
+ 1. Roger B. Nelsen. `An Introduction to Copulas'. Springer, New
+ York, second edition, 2006.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 60
+Compute the probability density function of a copula family.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 9
+copularnd
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1852
+ -- Function File: X = copularnd (FAMILY, THETA, N)
+ -- Function File: copularnd (FAMILY, THETA, N, D)
+ -- Function File: copularnd ('t', THETA, NU, N)
+ Generate random samples from a copula family.
+
+Arguments
+---------
+
+ * FAMILY is the copula family name. Currently, FAMILY can be
+ `'Gaussian'' for the Gaussian family, `'t'' for the Student's
+ t family, or `'Clayton'' for the Clayton family.
+
+ * THETA is the parameter of the copula. For the Gaussian and
+ Student's t copula, THETA must be a correlation matrix. For
+ bivariate copulas THETA can also be a correlation
+ coefficient. For the Clayton family, THETA must be a vector
+ with the same number of elements as samples to be generated
+ or be scalar.
+
+ * NU is the degrees of freedom for the Student's t family. NU
+ must be a vector with the same number of elements as samples
+ to be generated or be scalar.
+
+ * N is the number of rows of the matrix to be generated. N must
+ be a non-negative integer and corresponds to the number of
+ samples to be generated.
+
+ * D is the number of columns of the matrix to be generated. D
+ must be a positive integer and corresponds to the dimension
+ of the copula.
+
+Return values
+-------------
+
+ * X is a matrix of random samples from the copula with N samples
+ of distribution dimension D.
+
+Examples
+--------
+
+ theta = 0.5;
+ x = copularnd ("Gaussian", theta);
+
+ theta = 0.5;
+ nu = 2;
+ x = copularnd ("t", theta, nu);
+
+ theta = 0.5;
+ n = 2;
+ x = copularnd ("Clayton", theta, n);
+
+References
+----------
+
+ 1. Roger B. Nelsen. `An Introduction to Copulas'. Springer, New
+ York, second edition, 2006.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 45
+Generate random samples from a copula family.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+expstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 802
+ -- Function File: [M, V] = expstat (L)
+ Compute mean and variance of the exponential distribution.
+
+Arguments
+---------
+
+ * L is the parameter of the exponential distribution. The
+ elements of L must be positive
+
+Return values
+-------------
+
+ * M is the mean of the exponential distribution
+
+ * V is the variance of the exponential distribution
+
+Example
+-------
+
+ l = 1:6;
+ [m, v] = expstat (l)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 58
+Compute mean and variance of the exponential distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+ff2n
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 100
+ -- Function File: ff2n (N)
+ Full-factor design with n binary terms.
+
+ See also: fullfact
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 39
+Full-factor design with n binary terms.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+fstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1120
+ -- Function File: [MN, V] = fstat (M, N)
+ Compute mean and variance of the F distribution.
+
+Arguments
+---------
+
+ * M is the first parameter of the F distribution. The elements
+ of M must be positive
+
+ * N is the second parameter of the F distribution. The elements
+ of N must be positive
+ M and N must be of common size or one of them must be scalar
+
+Return values
+-------------
+
+ * MN is the mean of the F distribution. The mean is undefined
+ for N not greater than 2
+
+ * V is the variance of the F distribution. The variance is
+ undefined for N not greater than 4
+
+Examples
+--------
+
+ m = 1:6;
+ n = 5:10;
+ [mn, v] = fstat (m, n)
+
+ [mn, v] = fstat (m, 5)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 48
+Compute mean and variance of the F distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+fullfact
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 264
+ -- Function File: fullfact (N)
+ Full factorial design.
+
+ If N is a scalar, return the full factorial design with N binary
+ choices, 0 and 1.
+
+ If N is a vector, return the full factorial design with choices 1
+ through N_I for each factor I.
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 22
+Full factorial design.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+gamfit
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 170
+ -- Function File: [A B] = gamfit (R)
+ Finds the maximumlikelihood estimator for the Gamma distribution
+ for R
+
+ See also: gampdf, gaminv, gamrnd, gamlike
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 71
+Finds the maximumlikelihood estimator for the Gamma distribution for R
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+gamlike
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 226
+ -- Function File: X = gamlike ([A B], R)
+ Calculates the negative log-likelihood function for the Gamma
+ distribution over vector R, with the given parameters A and B.
+
+ See also: gampdf, gaminv, gamrnd, gamfit
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Calculates the negative log-likelihood function for the Gamma
+distribution over
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+gamstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 995
+ -- Function File: [M, V] = gamstat (A, B)
+ Compute mean and variance of the gamma distribution.
+
+Arguments
+---------
+
+ * A is the first parameter of the gamma distribution. A must be
+ positive
+
+ * B is the second parameter of the gamma distribution. B must be
+ positive
+ A and B must be of common size or one of them must be scalar
+
+Return values
+-------------
+
+ * M is the mean of the gamma distribution
+
+ * V is the variance of the gamma distribution
+
+Examples
+--------
+
+ a = 1:6;
+ b = 1:0.2:2;
+ [m, v] = gamstat (a, b)
+
+ [m, v] = gamstat (a, 1.5)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 52
+Compute mean and variance of the gamma distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+geomean
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 177
+ -- Function File: geomean (X)
+ -- Function File: geomean (X, DIM)
+ Compute the geometric mean.
+
+ This function does the same as `mean (x, "g")'.
+
+ See also: mean
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 27
+Compute the geometric mean.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+geostat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 811
+ -- Function File: [M, V] = geostat (P)
+ Compute mean and variance of the geometric distribution.
+
+Arguments
+---------
+
+ * P is the rate parameter of the geometric distribution. The
+ elements of P must be probabilities
+
+Return values
+-------------
+
+ * M is the mean of the geometric distribution
+
+ * V is the variance of the geometric distribution
+
+Example
+-------
+
+ p = 1 ./ (1:6);
+ [m, v] = geostat (p)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 56
+Compute mean and variance of the geometric distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+harmmean
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 178
+ -- Function File: harmmean (X)
+ -- Function File: harmmean (X, DIM)
+ Compute the harmonic mean.
+
+ This function does the same as `mean (x, "h")'.
+
+ See also: mean
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 26
+Compute the harmonic mean.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+histfit
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 412
+ -- Function File: histfit (DATA, NBINS)
+ Plot histogram with superimposed fitted normal density.
+
+ `histfit (DATA, NBINS)' plots a histogram of the values in the
+ vector DATA using NBINS bars in the histogram. With one input
+ argument, NBINS is set to the square root of the number of
+ elements in data.
+
+ Example
+
+ histfit (randn (100, 1))
+
+ See also: bar, hist, pareto
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 55
+Plot histogram with superimposed fitted normal density.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 11
+hmmestimate
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4098
+ -- Function File: [TRANSPROBEST, OUTPROBEST] = hmmestimate (SEQUENCE,
+ STATES)
+ -- Function File: hmmestimate (..., 'statenames', STATENAMES)
+ -- Function File: hmmestimate (..., 'symbols', SYMBOLS)
+ -- Function File: hmmestimate (..., 'pseudotransitions',
+ PSEUDOTRANSITIONS)
+ -- Function File: hmmestimate (..., 'pseudoemissions',
+ PSEUDOEMISSIONS)
+ Estimate the matrix of transition probabilities and the matrix of
+ output probabilities of a given sequence of outputs and states
+ generated by a hidden Markov model. The model assumes that the
+ generation starts in state `1' at step `0' but does not include
+ step `0' in the generated states and sequence.
+
+Arguments
+---------
+
+ * SEQUENCE is a vector of a sequence of given outputs. The
+ outputs must be integers ranging from `1' to the number of
+ outputs of the hidden Markov model.
+
+ * STATES is a vector of the same length as SEQUENCE of given
+ states. The states must be integers ranging from `1' to the
+ number of states of the hidden Markov model.
+
+Return values
+-------------
+
+ * TRANSPROBEST is the matrix of the estimated transition
+ probabilities of the states. `transprobest(i, j)' is the
+ estimated probability of a transition to state `j' given
+ state `i'.
+
+ * OUTPROBEST is the matrix of the estimated output
+ probabilities. `outprobest(i, j)' is the estimated
+ probability of generating output `j' given state `i'.
+
+ If `'symbols'' is specified, then SEQUENCE is expected to be a
+sequence of the elements of SYMBOLS instead of integers. SYMBOLS can
+be a cell array.
+
+ If `'statenames'' is specified, then STATES is expected to be a
+sequence of the elements of STATENAMES instead of integers. STATENAMES
+can be a cell array.
+
+ If `'pseudotransitions'' is specified then the integer matrix
+PSEUDOTRANSITIONS is used as an initial number of counted transitions.
+`pseudotransitions(i, j)' is the initial number of counted transitions
+from state `i' to state `j'. TRANSPROBEST will have the same size as
+PSEUDOTRANSITIONS. Use this if you have transitions that are very
+unlikely to occur.
+
+ If `'pseudoemissions'' is specified then the integer matrix
+PSEUDOEMISSIONS is used as an initial number of counted outputs.
+`pseudoemissions(i, j)' is the initial number of counted outputs `j'
+given state `i'. If `'pseudoemissions'' is also specified then the
+number of rows of PSEUDOEMISSIONS must be the same as the number of
+rows of PSEUDOTRANSITIONS. OUTPROBEST will have the same size as
+PSEUDOEMISSIONS. Use this if you have outputs or states that are very
+unlikely to occur.
+
+Examples
+--------
+
+ transprob = [0.8, 0.2; 0.4, 0.6];
+ outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1];
+ [sequence, states] = hmmgenerate (25, transprob, outprob);
+ [transprobest, outprobest] = hmmestimate (sequence, states)
+
+ symbols = {'A', 'B', 'C'};
+ statenames = {'One', 'Two'};
+ [sequence, states] = hmmgenerate (25, transprob, outprob,
+ 'symbols', symbols, 'statenames', statenames);
+ [transprobest, outprobest] = hmmestimate (sequence, states,
+ 'symbols', symbols,
+ 'statenames', statenames)
+
+ pseudotransitions = [8, 2; 4, 6];
+ pseudoemissions = [2, 4, 4; 7, 2, 1];
+ [sequence, states] = hmmgenerate (25, transprob, outprob);
+ [transprobest, outprobest] = hmmestimate (sequence, states, 'pseudotransitions', pseudotransitions, 'pseudoemissions', pseudoemissions)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Lawrence R. Rabiner. A Tutorial on Hidden Markov Models and
+ Selected Applications in Speech Recognition. `Proceedings of
+ the IEEE', 77(2), pages 257-286, February 1989.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Estimate the matrix of transition probabilities and the matrix of output
+probabi
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 11
+hmmgenerate
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2406
+ -- Function File: [SEQUENCE, STATES] = hmmgenerate (LEN, TRANSPROB,
+ OUTPROB)
+ -- Function File: hmmgenerate (..., 'symbols', SYMBOLS)
+ -- Function File: hmmgenerate (..., 'statenames', STATENAMES)
+ Generate an output sequence and hidden states of a hidden Markov
+ model. The model starts in state `1' at step `0' but will not
+ include step `0' in the generated states and sequence.
+
+Arguments
+---------
+
+ * LEN is the number of steps to generate. SEQUENCE and STATES
+ will have LEN entries each.
+
+ * TRANSPROB is the matrix of transition probabilities of the
+ states. `transprob(i, j)' is the probability of a transition
+ to state `j' given state `i'.
+
+ * OUTPROB is the matrix of output probabilities. `outprob(i,
+ j)' is the probability of generating output `j' given state
+ `i'.
+
+Return values
+-------------
+
+ * SEQUENCE is a vector of length LEN of the generated outputs.
+ The outputs are integers ranging from `1' to `columns
+ (outprob)'.
+
+ * STATES is a vector of length LEN of the generated hidden
+ states. The states are integers ranging from `1' to `columns
+ (transprob)'.
+
+ If `'symbols'' is specified, then the elements of SYMBOLS are used
+for the output sequence instead of integers ranging from `1' to
+`columns (outprob)'. SYMBOLS can be a cell array.
+
+ If `'statenames'' is specified, then the elements of STATENAMES
+are used for the states instead of integers ranging from `1' to
+`columns (transprob)'. STATENAMES can be a cell array.
+
+Examples
+--------
+
+ transprob = [0.8, 0.2; 0.4, 0.6];
+ outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1];
+ [sequence, states] = hmmgenerate (25, transprob, outprob)
+
+ symbols = {'A', 'B', 'C'};
+ statenames = {'One', 'Two'};
+ [sequence, states] = hmmgenerate (25, transprob, outprob,
+ 'symbols', symbols, 'statenames', statenames)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Lawrence R. Rabiner. A Tutorial on Hidden Markov Models and
+ Selected Applications in Speech Recognition. `Proceedings of
+ the IEEE', 77(2), pages 257-286, February 1989.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 71
+Generate an output sequence and hidden states of a hidden Markov model.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 10
+hmmviterbi
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2559
+ -- Function File: VPATH = hmmviterbi (SEQUENCE, TRANSPROB, OUTPROB)
+ -- Function File: hmmviterbi (..., 'symbols', SYMBOLS)
+ -- Function File: hmmviterbi (..., 'statenames', STATENAMES)
+ Use the Viterbi algorithm to find the Viterbi path of a hidden
+ Markov model given a sequence of outputs. The model assumes that
+ the generation starts in state `1' at step `0' but does not
+ include step `0' in the generated states and sequence.
+
+Arguments
+---------
+
+ * SEQUENCE is the vector of length LEN of given outputs. The
+ outputs must be integers ranging from `1' to `columns
+ (outprob)'.
+
+ * TRANSPROB is the matrix of transition probabilities of the
+ states. `transprob(i, j)' is the probability of a transition
+ to state `j' given state `i'.
+
+ * OUTPROB is the matrix of output probabilities. `outprob(i,
+ j)' is the probability of generating output `j' given state
+ `i'.
+
+Return values
+-------------
+
+ * VPATH is the vector of the same length as SEQUENCE of the
+ estimated hidden states. The states are integers ranging from
+ `1' to `columns (transprob)'.
+
+ If `'symbols'' is specified, then SEQUENCE is expected to be a
+sequence of the elements of SYMBOLS instead of integers ranging from
+`1' to `columns (outprob)'. SYMBOLS can be a cell array.
+
+ If `'statenames'' is specified, then the elements of STATENAMES
+are used for the states in VPATH instead of integers ranging from `1'
+to `columns (transprob)'. STATENAMES can be a cell array.
+
+Examples
+--------
+
+ transprob = [0.8, 0.2; 0.4, 0.6];
+ outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1];
+ [sequence, states] = hmmgenerate (25, transprob, outprob)
+ vpath = hmmviterbi (sequence, transprob, outprob)
+
+ symbols = {'A', 'B', 'C'};
+ statenames = {'One', 'Two'};
+ [sequence, states] = hmmgenerate (25, transprob, outprob,
+ 'symbols', symbols, 'statenames', statenames)
+ vpath = hmmviterbi (sequence, transprob, outprob,
+ 'symbols', symbols, 'statenames', statenames)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Lawrence R. Rabiner. A Tutorial on Hidden Markov Models and
+ Selected Applications in Speech Recognition. `Proceedings of
+ the IEEE', 77(2), pages 257-286, February 1989.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Use the Viterbi algorithm to find the Viterbi path of a hidden Markov
+model give
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+hygestat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1290
+ -- Function File: [MN, V] = hygestat (T, M, N)
+ Compute mean and variance of the hypergeometric distribution.
+
+Arguments
+---------
+
+ * T is the total size of the population of the hypergeometric
+ distribution. The elements of T must be positive natural
+ numbers
+
+ * M is the number of marked items of the hypergeometric
+ distribution. The elements of M must be natural numbers
+
+ * N is the size of the drawn sample of the hypergeometric
+ distribution. The elements of N must be positive natural
+ numbers
+ T, M, and N must be of common size or scalar
+
+Return values
+-------------
+
+ * MN is the mean of the hypergeometric distribution
+
+ * V is the variance of the hypergeometric distribution
+
+Examples
+--------
+
+ t = 4:9;
+ m = 0:5;
+ n = 1:6;
+ [mn, v] = hygestat (t, m, n)
+
+ [mn, v] = hygestat (t, m, 2)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 61
+Compute mean and variance of the hypergeometric distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 9
+jackknife
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2008
+ -- Function File: JACKSTAT = jackknife (E, X, ...)
+ Compute jackknife estimates of a parameter taking one or more
+ given samples as parameters. In particular, E is the estimator to
+ be jackknifed as a function name, handle, or inline function, and
+ X is the sample for which the estimate is to be taken. The I-th
+ entry of JACKSTAT will contain the value of the estimator on the
+ sample X with its I-th row omitted.
+
+ jackstat(I) = E(X(1 : I - 1, I + 1 : length(X)))
+
+ Depending on the number of samples to be used, the estimator must
+ have the appropriate form: If only one sample is used, then the
+ estimator need not be concerned with cell arrays, for example
+ jackknifing the standard deviation of a sample can be performed
+ with `JACKSTAT = jackknife (@std, rand (100, 1))'. If, however,
+ more than one sample is to be used, the samples must all be of
+ equal size, and the estimator must address them as elements of a
+ cell-array, in which they are aggregated in their order of
+ appearance:
+
+ JACKSTAT = jackknife(@(x) std(x{1})/var(x{2}), rand (100, 1), randn (100, 1)
+
+ If all goes well, a theoretical value P for the parameter is
+ already known, N is the sample size, `T = N * E(X) - (N - 1) *
+ mean(JACKSTAT)', and `V = sumsq(N * E(X) - (N - 1) * JACKSTAT - T)
+ / (N * (N - 1))', then `(T-P)/sqrt(V)' should follow a
+ t-distribution with N-1 degrees of freedom.
+
+ Jackknifing is a well known method to reduce bias; further details
+ can be found in:
+ * Rupert G. Miller: The jackknife-a review; Biometrika (1974)
+ 61(1): 1-15; doi:10.1093/biomet/61.1.1
+
+ * Rupert G. Miller: Jackknifing Variances; Ann. Math. Statist.
+ Volume 39, Number 2 (1968), 567-582;
+ doi:10.1214/aoms/1177698418
+
+ * M. H. Quenouille: Notes on Bias in Estimation; Biometrika
+ Vol. 43, No. 3/4 (Dec., 1956), pp. 353-360;
+ doi:10.1093/biomet/43.3-4.353
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Compute jackknife estimates of a parameter taking one or more given
+samples as p
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+jsucdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 263
+ -- Function File: jsucdf (X, ALPHA1, ALPHA2)
+ For each element of X, compute the cumulative distribution
+ function (CDF) at X of the Johnson SU distribution with shape
+ parameters ALPHA1 and ALPHA2.
+
+ Default values are ALPHA1 = 1, ALPHA2 = 1.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+For each element of X, compute the cumulative distribution function
+(CDF) at X o
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+jsupdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 259
+ -- Function File: jsupdf (X, ALPHA1, ALPHA2)
+ For each element of X, compute the probability density function
+ (PDF) at X of the Johnson SU distribution with shape parameters
+ ALPHA1 and ALPHA2.
+
+ Default values are ALPHA1 = 1, ALPHA2 = 1.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+For each element of X, compute the probability density function (PDF)
+at X of th
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+kmeans
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 135
+ -- Function File: [IDX, CENTERS] = kmeans (DATA, K, PARAM1, VALUE1,
+ ...)
+ K-means clustering.
+
+ See also: linkage
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 19
+K-means clustering.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+linkage
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2933
+ -- Function File: Y = linkage (D)
+ -- Function File: Y = linkage (D, METHOD)
+ -- Function File: Y = linkage (X, METHOD, METRIC)
+ -- Function File: Y = linkage (X, METHOD, ARGLIST)
+ Produce a hierarchical clustering dendrogram
+
+ D is the dissimilarity matrix relative to N observations,
+ formatted as a (n-1)*n/2x1 vector as produced by `pdist'.
+ Alternatively, X contains data formatted for input to `pdist',
+ METRIC is a metric for `pdist' and ARGLIST is a cell array
+ containing arguments that are passed to `pdist'.
+
+ `linkage' starts by putting each observation into a singleton
+ cluster and numbering those from 1 to N. Then it merges two
+ clusters, chosen according to METHOD, to create a new cluster
+ numbered N+1, and so on until all observations are grouped into a
+ single cluster numbered 2*N-1. Row M of the m-1x3 output matrix
+ relates to cluster n+m: the first two columns are the numbers of
+ the two component clusters and column 3 contains their distance.
+
+ METHOD defines the way the distance between two clusters is
+ computed and how they are recomputed when two clusters are merged:
+
+ `"single" (default)'
+ Distance between two clusters is the minimum distance between
+ two elements belonging each to one cluster. Produces a
+ cluster tree known as minimum spanning tree.
+
+ `"complete"'
+ Furthest distance between two elements belonging each to one
+ cluster.
+
+ `"average"'
+ Unweighted pair group method with averaging (UPGMA). The
+ mean distance between all pair of elements each belonging to
+ one cluster.
+
+ `"weighted"'
+ Weighted pair group method with averaging (WPGMA). When two
+ clusters A and B are joined together, the new distance to a
+ cluster C is the mean between distances A-C and B-C.
+
+ `"centroid"'
+ Unweighted Pair-Group Method using Centroids (UPGMC).
+ Assumes Euclidean metric. The distance between cluster
+ centroids, each centroid being the center of mass of a
+ cluster.
+
+ `"median"'
+ Weighted pair-group method using centroids (WPGMC). Assumes
+ Euclidean metric. Distance between cluster centroids. When
+ two clusters are joined together, the new centroid is the
+ midpoint between the joined centroids.
+
+ `"ward"'
+ Ward's sum of squared deviations about the group mean (ESS).
+ Also known as minimum variance or inner squared distance.
+ Assumes Euclidean metric. How much the moment of inertia of
+ the merged cluster exceeds the sum of those of the individual
+ clusters.
+
+ *Reference* Ward, J. H. Hierarchical Grouping to Optimize an
+ Objective Function J. Am. Statist. Assoc. 1963, 58, 236-244,
+ `http://iv.slis.indiana.edu/sw/data/ward.pdf'.
+
+ See also: pdist, squareform
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 45
+Produce a hierarchical clustering dendrogram
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+lognstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1035
+ -- Function File: [M, V] = lognstat (MU, SIGMA)
+ Compute mean and variance of the lognormal distribution.
+
+Arguments
+---------
+
+ * MU is the first parameter of the lognormal distribution
+
+ * SIGMA is the second parameter of the lognormal distribution.
+ SIGMA must be positive or zero
+ MU and SIGMA must be of common size or one of them must be scalar
+
+Return values
+-------------
+
+ * M is the mean of the lognormal distribution
+
+ * V is the variance of the lognormal distribution
+
+Examples
+--------
+
+ mu = 0:0.2:1;
+ sigma = 0.2:0.2:1.2;
+ [m, v] = lognstat (mu, sigma)
+
+ [m, v] = lognstat (0, sigma)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 56
+Compute mean and variance of the lognormal distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+mad
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 767
+ -- Function File: mad (X)
+ -- Function File: mad (X, FLAG)
+ -- Function File: mad (X, FLAG, DIM)
+ Compute the mean/median absolute deviation of X.
+
+ The mean absolute deviation is computed as
+
+ mean (abs (X - mean (X)))
+
+ and the median absolute deviation is computed as
+
+ median (abs (X - median (X)))
+
+ Elements of X containing NaN or NA values are ignored during
+ computations.
+
+ If FLAG is 0, the absolute mean deviation is computed, and if FLAG
+ is 1, the absolute median deviation is computed. By default FLAG
+ is 0.
+
+ This is done along the dimension DIM of X. If this variable is not
+ given, the mean/median absolute deviation s computed along the
+ smallest dimension of X.
+
+ See also: std
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 48
+Compute the mean/median absolute deviation of X.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+mnpdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1643
+ -- Function File: Y = mnpdf (X, P)
+ Compute the probability density function of the multinomial
+ distribution.
+
+Arguments
+---------
+
+ * X is vector with a single sample of a multinomial
+ distribution with parameter P or a matrix of random samples
+ from multinomial distributions. In the latter case, each row
+ of X is a sample from a multinomial distribution with the
+ corresponding row of P being its parameter.
+
+ * P is a vector with the probabilities of the categories or a
+ matrix with each row containing the probabilities of a
+ multinomial sample.
+
+Return values
+-------------
+
+ * Y is a vector of probabilites of the random samples X from the
+ multinomial distribution with corresponding parameter P. The
+ parameter N of the multinomial distribution is the sum of the
+ elements of each row of X. The length of Y is the number of
+ columns of X. If a row of P does not sum to `1', then the
+ corresponding element of Y will be `NaN'.
+
+Examples
+--------
+
+ x = [1, 4, 2];
+ p = [0.2, 0.5, 0.3];
+ y = mnpdf (x, p);
+
+ x = [1, 4, 2; 1, 0, 9];
+ p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8];
+ y = mnpdf (x, p);
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Merran Evans, Nicholas Hastings and Brian Peacock.
+ `Statistical Distributions'. pages 134-136, Wiley, New York,
+ third edition, 2000.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 73
+Compute the probability density function of the multinomial
+distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+mnrnd
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2172
+ -- Function File: X = mnrnd (N, P)
+ -- Function File: X = mnrnd (N, P, S)
+ Generate random samples from the multinomial distribution.
+
+Arguments
+---------
+
+ * N is the first parameter of the multinomial distribution. N
+ can be scalar or a vector containing the number of trials of
+ each multinomial sample. The elements of N must be
+ non-negative integers.
+
+ * P is the second parameter of the multinomial distribution. P
+ can be a vector with the probabilities of the categories or a
+ matrix with each row containing the probabilities of a
+ multinomial sample. If P has more than one row and N is
+ non-scalar, then the number of rows of P must match the
+ number of elements of N.
+
+ * S is the number of multinomial samples to be generated. S must
+ be a non-negative integer. If S is specified, then N must be
+ scalar and P must be a vector.
+
+Return values
+-------------
+
+ * X is a matrix of random samples from the multinomial
+ distribution with corresponding parameters N and P. Each row
+ corresponds to one multinomial sample. The number of columns,
+ therefore, corresponds to the number of columns of P. If S is
+ not specified, then the number of rows of X is the maximum of
+ the number of elements of N and the number of rows of P. If a
+ row of P does not sum to `1', then the corresponding row of X
+ will contain only `NaN' values.
+
+Examples
+--------
+
+ n = 10;
+ p = [0.2, 0.5, 0.3];
+ x = mnrnd (n, p);
+
+ n = 10 * ones (3, 1);
+ p = [0.2, 0.5, 0.3];
+ x = mnrnd (n, p);
+
+ n = (1:2)';
+ p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8];
+ x = mnrnd (n, p);
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Merran Evans, Nicholas Hastings and Brian Peacock.
+ `Statistical Distributions'. pages 134-136, Wiley, New York,
+ third edition, 2000.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 58
+Generate random samples from the multinomial distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 15
+monotone_smooth
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1745
+ -- Function File: YY = monotone_smooth (X, Y, H)
+ Produce a smooth monotone increasing approximation to a sampled
+ functional dependence y(x) using a kernel method (an Epanechnikov
+ smoothing kernel is applied to y(x); this is integrated to yield
+ the monotone increasing form. See Reference 1 for details.)
+
+Arguments
+---------
+
+ * X is a vector of values of the independent variable.
+
+ * Y is a vector of values of the dependent variable, of the
+ same size as X. For best performance, it is recommended that
+ the Y already be fairly smooth, e.g. by applying a kernel
+ smoothing to the original values if they are noisy.
+
+ * H is the kernel bandwidth to use. If H is not given, a
+ "reasonable" value is computed.
+
+
+Return values
+-------------
+
+ * YY is the vector of smooth monotone increasing function
+ values at X.
+
+
+Examples
+--------
+
+ x = 0:0.1:10;
+ y = (x .^ 2) + 3 * randn(size(x)); %typically non-monotonic from the added noise
+ ys = ([y(1) y(1:(end-1))] + y + [y(2:end) y(end)])/3; %crudely smoothed via
+ moving average, but still typically non-monotonic
+ yy = monotone_smooth(x, ys); %yy is monotone increasing in x
+ plot(x, y, '+', x, ys, x, yy)
+
+References
+----------
+
+ 1. Holger Dette, Natalie Neumeyer and Kay F. Pilz (2006), A
+ simple nonparametric estimator of a strictly monotone
+ regression function, `Bernoulli', 12:469-490
+
+ 2. Regine Scheder (2007), R Package 'monoProc', Version 1.0-6,
+ `http://cran.r-project.org/web/packages/monoProc/monoProc.pdf'
+ (The implementation here is based on the monoProc function
+ mono.1d)
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Produce a smooth monotone increasing approximation to a sampled
+functional depen
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+mvncdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1188
+ -- Function File: P = mvncdf (X, MU, SIGMA)
+ -- Function File: mvncdf (A, X, MU, SIGMA)
+ -- Function File: [P, ERR] = mvncdf (...)
+ Compute the cumulative distribution function of the multivariate
+ normal distribution.
+
+Arguments
+---------
+
+ * X is the upper limit for integration where each row
+ corresponds to an observation.
+
+ * MU is the mean.
+
+ * SIGMA is the correlation matrix.
+
+ * A is the lower limit for integration where each row
+ corresponds to an observation. A must have the same size as X.
+
+Return values
+-------------
+
+ * P is the cumulative distribution at each row of X and A.
+
+ * ERR is the estimated error.
+
+Examples
+--------
+
+ x = [1 2];
+ mu = [0.5 1.5];
+ sigma = [1.0 0.5; 0.5 1.0];
+ p = mvncdf (x, mu, sigma)
+
+ a = [-inf 0];
+ p = mvncdf (a, x, mu, sigma)
+
+References
+----------
+
+ 1. Alan Genz and Frank Bretz. Numerical Computation of
+ Multivariate t-Probabilities with Application to Power
+ Calculation of Multiple Constrasts. `Journal of Statistical
+ Computation and Simulation', 63, pages 361-378, 1999.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Compute the cumulative distribution function of the multivariate normal
+distribu
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+mvnpdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1600
+ -- Function File: Y = mvnpdf (X)
+ -- Function File: Y = mvnpdf (X, MU)
+ -- Function File: Y = mvnpdf (X, MU, SIGMA)
+ Compute multivariate normal pdf for X given mean MU and covariance
+ matrix SIGMA. The dimension of X is D x P, MU is 1 x P and SIGMA
+ is P x P. The normal pdf is defined as
+
+ 1/Y^2 = (2 pi)^P |SIGMA| exp { (X-MU)' inv(SIGMA) (X-MU) }
+
+ *References*
+
+ NIST Engineering Statistics Handbook 6.5.4.2
+ http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc542.htm
+
+ *Algorithm*
+
+ Using Cholesky factorization on the positive definite covariance
+ matrix:
+
+ R = chol (SIGMA);
+
+ where R'*R = SIGMA. Being upper triangular, the determinant of R
+ is trivially the product of the diagonal, and the determinant of
+ SIGMA is the square of this:
+
+ DET = prod (diag (R))^2;
+
+ The formula asks for the square root of the determinant, so no
+ need to square it.
+
+ The exponential argument A = X' * inv (SIGMA) * X
+
+ A = X' * inv (SIGMA) * X
+ = X' * inv (R' * R) * X
+ = X' * inv (R) * inv(R') * X
+
+ Given that inv (R') == inv(R)', at least in theory if not
+ numerically,
+
+ A = (X' / R) * (X'/R)' = sumsq (X'/R)
+
+ The interface takes the parameters to the multivariate normal in
+ columns rather than rows, so we are actually dealing with the
+ transpose:
+
+ A = sumsq (X/r)
+
+ and the final result is:
+
+ R = chol (SIGMA)
+ Y = (2*pi)^(-P/2) * exp (-sumsq ((X-MU)/R, 2)/2) / prod (diag (R))
+
+ See also: mvncdf, mvnrnd
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Compute multivariate normal pdf for X given mean MU and covariance
+matrix SIGMA.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+mvnrnd
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 228
+ -- Function File: S = mvnrnd (MU, SIGMA)
+ -- Function File: S = mvnrnd (MU, SIGMA, N)
+ Draw N random D-dimensional vectors from a multivariate Gaussian
+ distribution with mean MU(NxD) and covariance matrix SIGMA(DxD).
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Draw N random D-dimensional vectors from a multivariate Gaussian
+distribution wi
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+mvtcdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1199
+ -- Function File: P = mvtcdf (X, SIGMA, NU)
+ -- Function File: mvtcdf (A, X, SIGMA, NU)
+ -- Function File: [P, ERR] = mvtcdf (...)
+ Compute the cumulative distribution function of the multivariate
+ Student's t distribution.
+
+Arguments
+---------
+
+ * X is the upper limit for integration where each row
+ corresponds to an observation.
+
+ * SIGMA is the correlation matrix.
+
+ * NU is the degrees of freedom.
+
+ * A is the lower limit for integration where each row
+ corresponds to an observation. A must have the same size as X.
+
+Return values
+-------------
+
+ * P is the cumulative distribution at each row of X and A.
+
+ * ERR is the estimated error.
+
+Examples
+--------
+
+ x = [1 2];
+ sigma = [1.0 0.5; 0.5 1.0];
+ nu = 4;
+ p = mvtcdf (x, sigma, nu)
+
+ a = [-inf 0];
+ p = mvtcdf (a, x, sigma, nu)
+
+References
+----------
+
+ 1. Alan Genz and Frank Bretz. Numerical Computation of
+ Multivariate t-Probabilities with Application to Power
+ Calculation of Multiple Constrasts. `Journal of Statistical
+ Computation and Simulation', 63, pages 361-378, 1999.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Compute the cumulative distribution function of the multivariate
+Student's t dis
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+mvtrnd
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1436
+ -- Function File: X = mvtrnd (SIGMA, NU)
+ -- Function File: X = mvtrnd (SIGMA, NU, N)
+ Generate random samples from the multivariate t-distribution.
+
+Arguments
+---------
+
+ * SIGMA is the matrix of correlation coefficients. If there are
+ any non-unit diagonal elements then SIGMA will be normalized.
+
+ * NU is the degrees of freedom for the multivariate
+ t-distribution. NU must be a vector with the same number of
+ elements as samples to be generated or be scalar.
+
+ * N is the number of rows of the matrix to be generated. N must
+ be a non-negative integer and corresponds to the number of
+ samples to be generated.
+
+Return values
+-------------
+
+ * X is a matrix of random samples from the multivariate
+ t-distribution with N row samples.
+
+Examples
+--------
+
+ sigma = [1, 0.5; 0.5, 1];
+ nu = 3;
+ n = 10;
+ x = mvtrnd (sigma, nu, n);
+
+ sigma = [1, 0.5; 0.5, 1];
+ nu = [2; 3];
+ n = 2;
+ x = mvtrnd (sigma, nu, 2);
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Samuel Kotz and Saralees Nadarajah. `Multivariate t
+ Distributions and Their Applications'. Cambridge University
+ Press, Cambridge, 2004.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 61
+Generate random samples from the multivariate t-distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+nanmax
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 379
+ -- Function File: [V, IDX] = nanmax (X)
+ -- Function File: [V, IDX] = nanmax (X, Y)
+ Find the maximal element while ignoring NaN values.
+
+ `nanmax' is identical to the `max' function except that NaN values
+ are ignored. If all values in a column are NaN, the maximum is
+ returned as NaN rather than [].
+
+ See also: max, nansum, nanmin, nanmean, nanmedian
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 51
+Find the maximal element while ignoring NaN values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+nanmean
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 339
+ -- Function File: V = nanmean (X)
+ -- Function File: V = nanmean (X, DIM)
+ Compute the mean value while ignoring NaN values.
+
+ `nanmean' is identical to the `mean' function except that NaN
+ values are ignored. If all values are NaN, the mean is returned
+ as NaN.
+
+ See also: mean, nanmin, nanmax, nansum, nanmedian
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 49
+Compute the mean value while ignoring NaN values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 9
+nanmedian
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 355
+ -- Function File: V = nanmedian (X)
+ -- Function File: V = nanmedian (X, DIM)
+ Compute the median of data while ignoring NaN values.
+
+ This function is identical to the `median' function except that
+ NaN values are ignored. If all values are NaN, the median is
+ returned as NaN.
+
+ See also: median, nanmin, nanmax, nansum, nanmean
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 53
+Compute the median of data while ignoring NaN values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+nanmin
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 379
+ -- Function File: [V, IDX] = nanmin (X)
+ -- Function File: [V, IDX] = nanmin (X, Y)
+ Find the minimal element while ignoring NaN values.
+
+ `nanmin' is identical to the `min' function except that NaN values
+ are ignored. If all values in a column are NaN, the minimum is
+ returned as NaN rather than [].
+
+ See also: min, nansum, nanmax, nanmean, nanmedian
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 51
+Find the minimal element while ignoring NaN values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+nanstd
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 932
+ -- Function File: V = nanstd (X)
+ -- Function File: V = nanstd (X, OPT)
+ -- Function File: V = nanstd (X, OPT, DIM)
+ Compute the standard deviation while ignoring NaN values.
+
+ `nanstd' is identical to the `std' function except that NaN values
+ are ignored. If all values are NaN, the standard deviation is
+ returned as NaN. If there is only a single non-NaN value, the
+ deviation is returned as 0.
+
+ The argument OPT determines the type of normalization to use.
+ Valid values are
+
+ 0:
+ normalizes with N-1, provides the square root of best
+ unbiased estimator of the variance [default]
+
+ 1:
+ normalizes with N, this provides the square root of the
+ second moment around the mean
+
+ The third argument DIM determines the dimension along which the
+ standard deviation is calculated.
+
+ See also: std, nanmin, nanmax, nansum, nanmedian, nanmean
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 57
+Compute the standard deviation while ignoring NaN values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+nansum
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 345
+ -- Function File: V = nansum (X)
+ -- Function File: V = nansum (X, DIM)
+ Compute the sum while ignoring NaN values.
+
+ `nansum' is identical to the `sum' function except that NaN values
+ are treated as 0 and so ignored. If all values are NaN, the sum is
+ returned as 0.
+
+ See also: sum, nanmin, nanmax, nanmean, nanmedian
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 42
+Compute the sum while ignoring NaN values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+nanvar
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 783
+ -- Function File: nanvar (X)
+ -- Function File: V = nanvar (X, OPT)
+ -- Function File: V = nanvar (X, OPT, DIM)
+ Compute the variance while ignoring NaN values.
+
+ For vector arguments, return the (real) variance of the values.
+ For matrix arguments, return a row vector containing the variance
+ for each column.
+
+ The argument OPT determines the type of normalization to use.
+ Valid values are
+
+ 0:
+ Normalizes with N-1, provides the best unbiased estimator of
+ the variance [default].
+
+ 1:
+ Normalizes with N, this provides the second moment around the
+ mean.
+
+ The third argument DIM determines the dimension along which the
+ variance is calculated.
+
+ See also: var, nanmean, nanstd, nanmax, nanmin
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 47
+Compute the variance while ignoring NaN values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+nbinstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1106
+ -- Function File: [M, V] = nbinstat (N, P)
+ Compute mean and variance of the negative binomial distribution.
+
+Arguments
+---------
+
+ * N is the first parameter of the negative binomial
+ distribution. The elements of N must be natural numbers
+
+ * P is the second parameter of the negative binomial
+ distribution. The elements of P must be probabilities
+ N and P must be of common size or one of them must be scalar
+
+Return values
+-------------
+
+ * M is the mean of the negative binomial distribution
+
+ * V is the variance of the negative binomial distribution
+
+Examples
+--------
+
+ n = 1:4;
+ p = 0.2:0.2:0.8;
+ [m, v] = nbinstat (n, p)
+
+ [m, v] = nbinstat (n, 0.5)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 64
+Compute mean and variance of the negative binomial distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 22
+normalise_distribution
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2097
+ -- Function File: NORMALISED = normalise_distribution (DATA)
+ -- Function File: NORMALISED = normalise_distribution (DATA,
+ DISTRIBUTION)
+ -- Function File: NORMALISED = normalise_distribution (DATA,
+ DISTRIBUTION, DIMENSION)
+ Transform a set of data so as to be N(0,1) distributed according
+ to an idea by van Albada and Robinson. This is achieved by first
+ passing it through its own cumulative distribution function (CDF)
+ in order to get a uniform distribution, and then mapping the
+ uniform to a normal distribution. The data must be passed as a
+ vector or matrix in DATA. If the CDF is unknown, then [] can be
+ passed in DISTRIBUTION, and in this case the empirical CDF will be
+ used. Otherwise, if the CDFs for all data are known, they can be
+ passed in DISTRIBUTION, either in the form of a single function
+ name as a string, or a single function handle, or a cell array
+ consisting of either all function names as strings, or all
+ function handles. In the latter case, the number of CDFs passed
+ must match the number of rows, or columns respectively, to
+ normalise. If the data are passed as a matrix, then the
+ transformation will operate either along the first non-singleton
+ dimension, or along DIMENSION if present.
+
+ Notes: The empirical CDF will map any two sets of data having the
+ same size and their ties in the same places after sorting to some
+ permutation of the same normalised data:
+ `normalise_distribution([1 2 2 3 4])'
+ => -1.28 0.00 0.00 0.52 1.28
+
+ `normalise_distribution([1 10 100 10 1000])'
+ => -1.28 0.00 0.52 0.00 1.28
+
+ Original source: S.J. van Albada, P.A. Robinson "Transformation of
+ arbitrary distributions to the normal distribution with
+ application to EEG test-retest reliability" Journal of
+ Neuroscience Methods, Volume 161, Issue 2, 15 April 2007, Pages
+ 205-211 ISSN 0165-0270, 10.1016/j.jneumeth.2006.11.004.
+ (http://www.sciencedirect.com/science/article/pii/S0165027006005668)
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Transform a set of data so as to be N(0,1) distributed according to an
+idea by v
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+normplot
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 445
+ -- Function File: normplot (X)
+ Produce a normal probability plot for each column of X.
+
+ The line joing the 1st and 3rd quantile is drawn on the graph. If
+ the underlying distribution is normal, the points will cluster
+ around this line.
+
+ Note that this function sets the title, xlabel, ylabel, axis,
+ grid, tics and hold properties of the graph. These need to be
+ cleared before subsequent graphs using 'clf'.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 55
+Produce a normal probability plot for each column of X.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+normstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 967
+ -- Function File: [MN, V] = normstat (M, S)
+ Compute mean and variance of the normal distribution.
+
+Arguments
+---------
+
+ * M is the mean of the normal distribution
+
+ * S is the standard deviation of the normal distribution. S
+ must be positive
+ M and S must be of common size or one of them must be scalar
+
+Return values
+-------------
+
+ * MN is the mean of the normal distribution
+
+ * V is the variance of the normal distribution
+
+Examples
+--------
+
+ m = 1:6;
+ s = 0:0.2:1;
+ [mn, v] = normstat (m, s)
+
+ [mn, v] = normstat (0, s)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 53
+Compute mean and variance of the normal distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+pdist
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2477
+ -- Function File: Y = pdist (X)
+ -- Function File: Y = pdist (X, METRIC)
+ -- Function File: Y = pdist (X, METRIC, METRICARG, ...)
+ Return the distance between any two rows in X.
+
+ X is the NxD matrix representing Q row vectors of size D.
+
+ The output is a dissimilarity matrix formatted as a row vector Y,
+ (n-1)*n/2 long, where the distances are in the order [(1, 2) (1,
+ 3) ... (2, 3) ... (n-1, n)]. You can use the `squareform'
+ function to display the distances between the vectors arranged
+ into an NxN matrix.
+
+ `metric' is an optional argument specifying how the distance is
+ computed. It can be any of the following ones, defaulting to
+ "euclidean", or a user defined function that takes two arguments X
+ and Y plus any number of optional arguments, where X is a row
+ vector and and Y is a matrix having the same number of columns as
+ X. `metric' returns a column vector where row I is the distance
+ between X and row I of Y. Any additional arguments after the
+ `metric' are passed as metric (X, Y, METRICARG1, METRICARG2 ...).
+
+ Predefined distance functions are:
+
+ `"euclidean"'
+ Euclidean distance (default).
+
+ `"seuclidean"'
+ Standardized Euclidean distance. Each coordinate in the sum of
+ squares is inverse weighted by the sample variance of that
+ coordinate.
+
+ `"mahalanobis"'
+ Mahalanobis distance: see the function mahalanobis.
+
+ `"cityblock"'
+ City Block metric, aka Manhattan distance.
+
+ `"minkowski"'
+ Minkowski metric. Accepts a numeric parameter P: for P=1
+ this is the same as the cityblock metric, with P=2 (default)
+ it is equal to the euclidean metric.
+
+ `"cosine"'
+ One minus the cosine of the included angle between rows, seen
+ as vectors.
+
+ `"correlation"'
+ One minus the sample correlation between points (treated as
+ sequences of values).
+
+ `"spearman"'
+ One minus the sample Spearman's rank correlation between
+ observations, treated as sequences of values.
+
+ `"hamming"'
+ Hamming distance: the quote of the number of coordinates that
+ differ.
+
+ `"jaccard"'
+ One minus the Jaccard coefficient, the quote of nonzero
+ coordinates that differ.
+
+ `"chebychev"'
+ Chebychev distance: the maximum coordinate difference.
+
+ See also: linkage, mahalanobis, squareform
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 46
+Return the distance between any two rows in X.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+poisstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 820
+ -- Function File: [M, V] = poisstat (LAMBDA)
+ Compute mean and variance of the Poisson distribution.
+
+Arguments
+---------
+
+ * LAMBDA is the parameter of the Poisson distribution. The
+ elements of LAMBDA must be positive
+
+Return values
+-------------
+
+ * M is the mean of the Poisson distribution
+
+ * V is the variance of the Poisson distribution
+
+Example
+-------
+
+ lambda = 1 ./ (1:6);
+ [m, v] = poisstat (lambda)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 54
+Compute mean and variance of the Poisson distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+princomp
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 332
+ -- Function File: [PC, Z, W, TSQ] = princomp (X)
+ Compute principal components of X.
+
+ The first output argument PC is the principal components of X.
+ The second Z is the transformed data, and W is the eigenvalues of
+ the covariance matrix of X. TSQ is the Hotelling's T^2 statistic
+ for the transformed data.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 34
+Compute principal components of X.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+random
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3107
+ -- Function File: R = random(NAME, ARG1)
+ -- Function File: R = random(NAME, ARG1, ARG2)
+ -- Function File: R = random(NAME, ARG1, ARG2, ARG3)
+ -- Function File: R = random(NAME, ..., S1, ...)
+ Generates pseudo-random numbers from a given one-, two-, or
+ three-parameter distribution.
+
+ The variable NAME must be a string that names the distribution from
+ which to sample. If this distribution is a one-parameter
+ distribution ARG1 should be supplied, if it is a two-paramter
+ distribution ARG2 must also be supplied, and if it is a
+ three-parameter distribution ARG3 must also be present. Any
+ arguments following the distribution paramters will determine the
+ size of the result.
+
+ As an example, the following code generates a 10 by 20 matrix
+ containing random numbers from a normal distribution with mean 5
+ and standard deviation 2.
+ R = random("normal", 5, 2, [10, 20]);
+
+ The variable NAME can be one of the following strings
+
+ "beta"
+ "beta distribution"
+ Samples are drawn from the Beta distribution.
+
+ "bino"
+ "binomial"
+ "binomial distribution"
+ Samples are drawn from the Binomial distribution.
+
+ "chi2"
+ "chi-square"
+ "chi-square distribution"
+ Samples are drawn from the Chi-Square distribution.
+
+ "exp"
+ "exponential"
+ "exponential distribution"
+ Samples are drawn from the Exponential distribution.
+
+ "f"
+ "f distribution"
+ Samples are drawn from the F distribution.
+
+ "gam"
+ "gamma"
+ "gamma distribution"
+ Samples are drawn from the Gamma distribution.
+
+ "geo"
+ "geometric"
+ "geometric distribution"
+ Samples are drawn from the Geometric distribution.
+
+ "hyge"
+ "hypergeometric"
+ "hypergeometric distribution"
+ Samples are drawn from the Hypergeometric distribution.
+
+ "logn"
+ "lognormal"
+ "lognormal distribution"
+ Samples are drawn from the Log-Normal distribution.
+
+ "nbin"
+ "negative binomial"
+ "negative binomial distribution"
+ Samples are drawn from the Negative Binomial distribution.
+
+ "norm"
+ "normal"
+ "normal distribution"
+ Samples are drawn from the Normal distribution.
+
+ "poiss"
+ "poisson"
+ "poisson distribution"
+ Samples are drawn from the Poisson distribution.
+
+ "rayl"
+ "rayleigh"
+ "rayleigh distribution"
+ Samples are drawn from the Rayleigh distribution.
+
+ "t"
+ "t distribution"
+ Samples are drawn from the T distribution.
+
+ "unif"
+ "uniform"
+ "uniform distribution"
+ Samples are drawn from the Uniform distribution.
+
+ "unid"
+ "discrete uniform"
+ "discrete uniform distribution"
+ Samples are drawn from the Uniform Discrete distribution.
+
+ "wbl"
+ "weibull"
+ "weibull distribution"
+ Samples are drawn from the Weibull distribution.
+
+ See also: rand, betarnd, binornd, chi2rnd, exprnd, frnd, gamrnd,
+ geornd, hygernd, lognrnd, nbinrnd, normrnd, poissrnd, raylrnd,
+ trnd, unifrnd, unidrnd, wblrnd
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Generates pseudo-random numbers from a given one-, two-, or
+three-parameter dist
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+raylcdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1076
+ -- Function File: P = raylcdf (X, SIGMA)
+ Compute the cumulative distribution function of the Rayleigh
+ distribution.
+
+Arguments
+---------
+
+ * X is the support. The elements of X must be non-negative.
+
+ * SIGMA is the parameter of the Rayleigh distribution. The
+ elements of SIGMA must be positive.
+ X and SIGMA must be of common size or one of them must be scalar.
+
+Return values
+-------------
+
+ * P is the cumulative distribution of the Rayleigh distribution
+ at each element of X and corresponding parameter SIGMA.
+
+Examples
+--------
+
+ x = 0:0.5:2.5;
+ sigma = 1:6;
+ p = raylcdf (x, sigma)
+
+ p = raylcdf (x, 0.5)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. pages 104 and 148, McGraw-Hill, New
+ York, second edition, 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 74
+Compute the cumulative distribution function of the Rayleigh
+distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+raylinv
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1133
+ -- Function File: X = raylinv (P, SIGMA)
+ Compute the quantile of the Rayleigh distribution. The quantile is
+ the inverse of the cumulative distribution function.
+
+Arguments
+---------
+
+ * P is the cumulative distribution. The elements of P must be
+ probabilities.
+
+ * SIGMA is the parameter of the Rayleigh distribution. The
+ elements of SIGMA must be positive.
+ P and SIGMA must be of common size or one of them must be scalar.
+
+Return values
+-------------
+
+ * X is the quantile of the Rayleigh distribution at each
+ element of P and corresponding parameter SIGMA.
+
+Examples
+--------
+
+ p = 0:0.1:0.5;
+ sigma = 1:6;
+ x = raylinv (p, sigma)
+
+ x = raylinv (p, 0.5)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. pages 104 and 148, McGraw-Hill, New
+ York, second edition, 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 50
+Compute the quantile of the Rayleigh distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+raylpdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1068
+ -- Function File: Y = raylpdf (X, SIGMA)
+ Compute the probability density function of the Rayleigh
+ distribution.
+
+Arguments
+---------
+
+ * X is the support. The elements of X must be non-negative.
+
+ * SIGMA is the parameter of the Rayleigh distribution. The
+ elements of SIGMA must be positive.
+ X and SIGMA must be of common size or one of them must be scalar.
+
+Return values
+-------------
+
+ * Y is the probability density of the Rayleigh distribution at
+ each element of X and corresponding parameter SIGMA.
+
+Examples
+--------
+
+ x = 0:0.5:2.5;
+ sigma = 1:6;
+ y = raylpdf (x, sigma)
+
+ y = raylpdf (x, 0.5)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. pages 104 and 148, McGraw-Hill, New
+ York, second edition, 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 70
+Compute the probability density function of the Rayleigh distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+raylrnd
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1489
+ -- Function File: X = raylrnd (SIGMA)
+ -- Function File: X = raylrnd (SIGMA, SZ)
+ -- Function File: X = raylrnd (SIGMA, R, C)
+ Generate a matrix of random samples from the Rayleigh distribution.
+
+Arguments
+---------
+
+ * SIGMA is the parameter of the Rayleigh distribution. The
+ elements of SIGMA must be positive.
+
+ * SZ is the size of the matrix to be generated. SZ must be a
+ vector of non-negative integers.
+
+ * R is the number of rows of the matrix to be generated. R must
+ be a non-negative integer.
+
+ * C is the number of columns of the matrix to be generated. C
+ must be a non-negative integer.
+
+Return values
+-------------
+
+ * X is a matrix of random samples from the Rayleigh
+ distribution with corresponding parameter SIGMA. If neither
+ SZ nor R and C are specified, then X is of the same size as
+ SIGMA.
+
+Examples
+--------
+
+ sigma = 1:6;
+ x = raylrnd (sigma)
+
+ sz = [2, 3];
+ x = raylrnd (0.5, sz)
+
+ r = 2;
+ c = 3;
+ x = raylrnd (0.5, r, c)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. pages 104 and 148, McGraw-Hill, New
+ York, second edition, 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 67
+Generate a matrix of random samples from the Rayleigh distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+raylstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 815
+ -- Function File: [M, V] = raylstat (SIGMA)
+ Compute mean and variance of the Rayleigh distribution.
+
+Arguments
+---------
+
+ * SIGMA is the parameter of the Rayleigh distribution. The
+ elements of SIGMA must be positive.
+
+Return values
+-------------
+
+ * M is the mean of the Rayleigh distribution.
+
+ * V is the variance of the Rayleigh distribution.
+
+Example
+-------
+
+ sigma = 1:6;
+ [m, v] = raylstat (sigma)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 55
+Compute mean and variance of the Rayleigh distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+regress
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1333
+ -- Function File: [B, BINT, R, RINT, STATS] = regress (Y, X, [ALPHA])
+ Multiple Linear Regression using Least Squares Fit of Y on X with
+ the model `y = X * beta + e'.
+
+ Here,
+
+ * `y' is a column vector of observed values
+
+ * `X' is a matrix of regressors, with the first column filled
+ with the constant value 1
+
+ * `beta' is a column vector of regression parameters
+
+ * `e' is a column vector of random errors
+
+ Arguments are
+
+ * Y is the `y' in the model
+
+ * X is the `X' in the model
+
+ * ALPHA is the significance level used to calculate the
+ confidence intervals BINT and RINT (see `Return values'
+ below). If not specified, ALPHA defaults to 0.05
+
+ Return values are
+
+ * B is the `beta' in the model
+
+ * BINT is the confidence interval for B
+
+ * R is a column vector of residuals
+
+ * RINT is the confidence interval for R
+
+ * STATS is a row vector containing:
+
+ * The R^2 statistic
+
+ * The F statistic
+
+ * The p value for the full model
+
+ * The estimated error variance
+
+ R and RINT can be passed to `rcoplot' to visualize the residual
+ intervals and identify outliers.
+
+ NaN values in Y and X are removed before calculation begins.
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Multiple Linear Regression using Least Squares Fit of Y on X with the
+model `y =
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+repanova
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 696
+ -- Function File: [PVAL, TABLE, ST] = repanova (X, COND)
+ -- Function File: [PVAL, TABLE, ST] = repanova (X, COND, ['string' |
+ 'cell'])
+ Perform a repeated measures analysis of variance (Repeated ANOVA).
+ X is formated such that each row is a subject and each column is a
+ condition.
+
+ condition is typically a point in time, say t=1 then t=2, etc
+ condition can also be thought of as groups.
+
+ The optional flag can be either 'cell' or 'string' and reflects
+ the format of the table returned. Cell is the default.
+
+ NaNs are ignored using nanmean and nanstd.
+
+ This fuction does not currently support multiple columns of the
+ same condition!
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 66
+Perform a repeated measures analysis of variance (Repeated ANOVA).
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 10
+squareform
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 384
+ -- Function File: Y = squareform (X)
+ -- Function File: Y = squareform (X, "tovector")
+ -- Function File: Y = squareform (X, "tomatrix")
+ Convert a vector from the pdist function into a square matrix or
+ from a square matrix back to the vector form.
+
+ The second argument is used to specify the output type in case
+ there is a single element.
+
+ See also: pdist
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Convert a vector from the pdist function into a square matrix or from a
+square m
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+tabulate
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1886
+ -- Function File: TABLE = tabulate (DATA, EDGES)
+ Compute a frequency table.
+
+ For vector data, the function counts the number of values in data
+ that fall between the elements in the edges vector (which must
+ contain monotonically non-decreasing values). TABLE is a matrix.
+ The first column of TABLE is the number of bin, the second is the
+ number of instances in each class (absolute frequency). The third
+ column contains the percentage of each value (relative frequency)
+ and the fourth column contains the cumulative frequency.
+
+ If EDGES is missed the width of each class is unitary, if EDGES is
+ a scalar then represent the number of classes, or you can define
+ the width of each bin. TABLE(K, 2) will count the value DATA (I)
+ if EDGES (K) <= DATA (I) < EDGES (K+1). The last bin will count
+ the value of DATA (I) if EDGES(K) <= DATA (I) <= EDGES (K+1).
+ Values outside the values in EDGES are not counted. Use -inf and
+ inf in EDGES to include all values. Tabulate with no output
+ arguments returns a formatted table in the command window.
+
+ Example
+
+ sphere_radius = [1:0.05:2.5];
+ tabulate (sphere_radius)
+
+ Tabulate returns 2 bins, the first contains the sphere with radius
+ between 1 and 2 mm excluded, and the second one contains the
+ sphere with radius between 2 and 3 mm.
+
+ tabulate (sphere_radius, 10)
+
+ Tabulate returns ten bins.
+
+ tabulate (sphere_radius, [1, 1.5, 2, 2.5])
+
+ Tabulate returns three bins, the first contains the sphere with
+ radius between 1 and 1.5 mm excluded, the second one contains the
+ sphere with radius between 1.5 and 2 mm excluded, and the third
+ contains the sphere with radius between 2 and 2.5 mm.
+
+ bar (table (:, 1), table (:, 2))
+
+ draw histogram.
+
+ See also: bar, pareto
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 26
+Compute a frequency table.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+tblread
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 776
+ -- Function File: [DATA, VARNAMES, CASENAMES] = tblread (FILENAME)
+ -- Function File: [DATA, VARNAMES, CASENAMES] = tblread (FILENAME,
+ DELIMETER)
+ Read tabular data from an ascii file.
+
+ DATA is read from an ascii data file named FILENAME with an
+ optional DELIMETER. The delimeter may be any single character or
+ * "space" " " (default)
+
+ * "tab" "\t"
+
+ * "comma" ","
+
+ * "semi" ";"
+
+ * "bar" "|"
+
+ The DATA is read starting at cell (2,2) where the VARNAMES form a
+ char matrix from the first row (starting at (1,2)) vertically
+ concatenated, and the CASENAMES form a char matrix read from the
+ first column (starting at (2,1)) vertically concatenated.
+
+ See also: tblwrite, csv2cell, cell2csv
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 37
+Read tabular data from an ascii file.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+tblwrite
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 765
+ -- Function File: tblwrite (DATA, VARNAMES, CASENAMES, FILENAME)
+ -- Function File: tblwrite (DATA, VARNAMES, CASENAMES, FILENAME,
+ DELIMETER)
+ Write tabular data to an ascii file.
+
+ DATA is written to an ascii data file named FILENAME with an
+ optional DELIMETER. The delimeter may be any single character or
+ * "space" " " (default)
+
+ * "tab" "\t"
+
+ * "comma" ","
+
+ * "semi" ";"
+
+ * "bar" "|"
+
+ The DATA is written starting at cell (2,2) where the VARNAMES are
+ a char matrix or cell vector written to the first row (starting at
+ (1,2)), and the CASENAMES are a char matrix (or cell vector)
+ written to the first column (starting at (2,1)).
+
+ See also: tblread, csv2cell, cell2csv
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 36
+Write tabular data to an ascii file.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+trimmean
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 387
+ -- Function File: A = trimmean (X, P)
+ Compute the trimmed mean.
+
+ The trimmed mean of X is defined as the mean of X excluding the
+ highest and lowest P percent of the data.
+
+ For example
+
+ mean ([-inf, 1:9, inf])
+
+ is NaN, while
+
+ trimmean ([-inf, 1:9, inf], 10)
+
+ excludes the infinite values, which make the result 5.
+
+ See also: mean
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 25
+Compute the trimmed mean.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+tstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 798
+ -- Function File: [M, V] = tstat (N)
+ Compute mean and variance of the t (Student) distribution.
+
+Arguments
+---------
+
+ * N is the parameter of the t (Student) distribution. The
+ elements of N must be positive
+
+Return values
+-------------
+
+ * M is the mean of the t (Student) distribution
+
+ * V is the variance of the t (Student) distribution
+
+Example
+-------
+
+ n = 3:8;
+ [m, v] = tstat (n)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 58
+Compute mean and variance of the t (Student) distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+unidstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 840
+ -- Function File: [M, V] = unidstat (N)
+ Compute mean and variance of the discrete uniform distribution.
+
+Arguments
+---------
+
+ * N is the parameter of the discrete uniform distribution. The
+ elements of N must be positive natural numbers
+
+Return values
+-------------
+
+ * M is the mean of the discrete uniform distribution
+
+ * V is the variance of the discrete uniform distribution
+
+Example
+-------
+
+ n = 1:6;
+ [m, v] = unidstat (n)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 63
+Compute mean and variance of the discrete uniform distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+unifstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1047
+ -- Function File: [M, V] = unifstat (A, B)
+ Compute mean and variance of the continuous uniform distribution.
+
+Arguments
+---------
+
+ * A is the first parameter of the continuous uniform
+ distribution
+
+ * B is the second parameter of the continuous uniform
+ distribution
+ A and B must be of common size or one of them must be scalar and A
+must be less than B
+
+Return values
+-------------
+
+ * M is the mean of the continuous uniform distribution
+
+ * V is the variance of the continuous uniform distribution
+
+Examples
+--------
+
+ a = 1:6;
+ b = 2:2:12;
+ [m, v] = unifstat (a, b)
+
+ [m, v] = unifstat (a, 10)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 65
+Compute mean and variance of the continuous uniform distribution.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+vmpdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 319
+ -- Function File: THETA = vmpdf (X, MU, K)
+ Evaluates the Von Mises probability density function.
+
+ The Von Mises distribution has probability density function
+ f (X) = exp (K * cos (X - MU)) / Z ,
+ where Z is a normalisation constant. By default, MU is 0 and K is
+ 1.
+
+ See also: vmrnd
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 53
+Evaluates the Von Mises probability density function.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+vmrnd
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 518
+ -- Function File: THETA = vmrnd (MU, K)
+ -- Function File: THETA = vmrnd (MU, K, SZ)
+ Draw random angles from a Von Mises distribution with mean MU and
+ concentration K.
+
+ The Von Mises distribution has probability density function
+ f (X) = exp (K * cos (X - MU)) / Z ,
+ where Z is a normalisation constant.
+
+ The output, THETA, is a matrix of size SZ containing random angles
+ drawn from the given Von Mises distribution. By default, MU is 0
+ and K is 1.
+
+ See also: vmpdf
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Draw random angles from a Von Mises distribution with mean MU and
+concentration
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+wblstat
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1050
+ -- Function File: [M, V] = wblstat (SCALE, SHAPE)
+ Compute mean and variance of the Weibull distribution.
+
+Arguments
+---------
+
+ * SCALE is the scale parameter of the Weibull distribution.
+ SCALE must be positive
+
+ * SHAPE is the shape parameter of the Weibull distribution.
+ SHAPE must be positive
+ SCALE and SHAPE must be of common size or one of them must be
+scalar
+
+Return values
+-------------
+
+ * M is the mean of the Weibull distribution
+
+ * V is the variance of the Weibull distribution
+
+Examples
+--------
+
+ scale = 3:8;
+ shape = 1:6;
+ [m, v] = wblstat (scale, shape)
+
+ [m, v] = wblstat (6, shape)
+
+References
+----------
+
+ 1. Wendy L. Martinez and Angel R. Martinez. `Computational
+ Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
+ Chapman & Hall/CRC, 2001.
+
+ 2. Athanasios Papoulis. `Probability, Random Variables, and
+ Stochastic Processes'. McGraw-Hill, New York, second edition,
+ 1984.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 54
+Compute mean and variance of the Weibull distribution.
+
+
+
+
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff