Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / lognstat.m

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+## Copyright (C) 2006, 2007 Arno Onken <asnelt@asnelt.org>
+##
+## 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{m}, @var{v}] =} lognstat (@var{mu}, @var{sigma})
+## Compute mean and variance of the lognormal distribution.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @item
+## @var{mu} is the first parameter of the lognormal distribution
+##
+## @item
+## @var{sigma} is the second parameter of the lognormal distribution.
+## @var{sigma} must be positive or zero
+## @end itemize
+## @var{mu} and @var{sigma} must be of common size or one of them must be
+## scalar
+##
+## @subheading Return values
+##
+## @itemize @bullet
+## @item
+## @var{m} is the mean of the lognormal distribution
+##
+## @item
+## @var{v} is the variance of the lognormal distribution
+## @end itemize
+##
+## @subheading Examples
+##
+## @example
+## @group
+## mu = 0:0.2:1;
+## sigma = 0.2:0.2:1.2;
+## [m, v] = lognstat (mu, sigma)
+## @end group
+##
+## @group
+## [m, v] = lognstat (0, sigma)
+## @end group
+## @end example
+##
+## @subheading References
+##
+## @enumerate
+## @item
+## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics
+## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC,
+## 2001.
+##
+## @item
+## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic
+## Processes}. McGraw-Hill, New York, second edition, 1984.
+## @end enumerate
+## @end deftypefn
+
+## Author: Arno Onken <asnelt@asnelt.org>
+## Description: Moments of the lognormal distribution
+
+function [m, v] = lognstat (mu, sigma)
+
+  # Check arguments
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  if (! isempty (mu) && ! ismatrix (mu))
+    error ("lognstat: mu must be a numeric matrix");
+  endif
+  if (! isempty (sigma) && ! ismatrix (sigma))
+    error ("lognstat: sigma must be a numeric matrix");
+  endif
+
+  if (! isscalar (mu) || ! isscalar (sigma))
+    [retval, mu, sigma] = common_size (mu, sigma);
+    if (retval > 0)
+      error ("lognstat: mu and sigma must be of common size or scalar");
+    endif
+  endif
+
+  # Calculate moments
+  m = exp (mu + (sigma .^ 2) ./ 2);
+  v = (exp (sigma .^ 2) - 1) .* exp (2 .* mu + sigma .^ 2);
+
+  # Continue argument check
+  k = find (! (sigma >= 0) | ! (sigma < Inf));
+  if (any (k))
+    m(k) = NaN;
+    v(k) = NaN;
+  endif
+
+endfunction
+
+%!test
+%! mu = 0:0.2:1;
+%! sigma = 0.2:0.2:1.2;
+%! [m, v] = lognstat (mu, sigma);
+%! expected_m = [1.0202, 1.3231, 1.7860, 2.5093,  3.6693,   5.5845];
+%! expected_v = [0.0425, 0.3038, 1.3823, 5.6447, 23.1345, 100.4437];
+%! assert (m, expected_m, 0.001);
+%! assert (v, expected_v, 0.001);
+
+%!test
+%! sigma = 0.2:0.2:1.2;
+%! [m, v] = lognstat (0, sigma);
+%! expected_m = [1.0202, 1.0833, 1.1972, 1.3771, 1.6487,  2.0544];
+%! expected_v = [0.0425, 0.2036, 0.6211, 1.7002, 4.6708, 13.5936];
+%! assert (m, expected_m, 0.001);
+%! assert (v, expected_v, 0.001);