--- /dev/null
+## Copyright (C) 2009 Levente Torok <TorokLev@gmail.com>
+##
+## This program is free software; you can redistribute it and/or modify it under
+## the terms of the GNU General Public License as published by the Free Software
+## Foundation; either version 3 of the License, or (at your option) any later
+## version.
+##
+## This program is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+## details.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+##
+## @deftypefn {Function File} {@var{CL} =} cl_multinom (@var{x}, @var{N}, @var{b}, @var{calculation_type} ) - Confidence level of multinomial portions
+## Returns confidence level of multinomial parameters estimated @math{ p = x / sum(x) } with predefined confidence interval @var{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. @var{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.
+##
+## @subheading Arguments
+## @itemize @bullet
+## @item @var{x} : int vector : sample frequencies bins
+## @item @var{N} : int : Population size that was sampled by x. If N<sum(x), infinite number assumed
+## @item @var{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
+## @item @var{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
+## @end itemize
+##
+## @subheading Returns
+## Confidence level.
+##
+## @subheading Example
+## CL = cl_multinom( [27;43;19;11], 10000, 0.05 )
+## returns 0.69 confidence level.
+##
+## @subheading 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
+##
+## @end deftypefn
+
+function CL = cl_multinom( x, N, b = .05, calculation_type = "bromaghin")
+
+ if (nargin < 2 || nargin > 4)
+ print_usage;
+ elseif (!ischar (calculation_type))
+ error ("Argument calculation_type must be a string");
+ endif
+
+ k = rows(x);
+ nn = sum(x);
+ p = x / nn;
+
+ if (isscalar( b ))
+ if (b==0) b=0.02; endif
+ b = ones( rows(x), 1 ) * b;
+
+ if (b<0) b=1 ./ max( x, 1 ); endif
+ endif
+ bb = b .* b;
+
+ if (N==nn)
+ CL = 1;
+ return;
+ endif
+
+ if (N<nn)
+ fpc = 1;
+ else
+ fpc = (N-1) / (N-nn); # finite population correction tag
+ endif
+
+ beta = p.*(1-p);
+
+ switch calculation_type
+ case {"cochran"}
+ t = sqrt( fpc * nn * bb ./ beta )
+ alpha = ( 1 - normcdf( t )) * 2
+
+ case {"bromaghin"}
+ t = sqrt( fpc * (nn * 2 * bb )./ ( beta - 2 * bb + sqrt( beta .* beta - bb .* ( 4*beta - 1 ))) );
+ alpha = ( 1 - normcdf( t )) * 2;
+
+ case {"agresti_cull"}
+ ts = fpc * nn * bb ./ beta ;
+ if ( k<=2 )
+ alpha = 1 - chi2cdf( ts, k-1 ); % adjusted Wilson interval
+ else
+ alpha = 1 - chi2cdf( ts/k, 1 ); % Goodman interval with Bonferroni argument
+ endif
+ otherwise
+ error ("Unknown calculation type '%s'", calculation_type);
+ endswitch
+
+ CL = 1 - max( alpha );
+
+endfunction
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