Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / nbinstat.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}] =} nbinstat (@var{n}, @var{p})
+## Compute mean and variance of the negative binomial distribution.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @item
+## @var{n} is the first parameter of the negative binomial distribution. The elements
+## of @var{n} must be natural numbers
+##
+## @item
+## @var{p} is the second parameter of the negative binomial distribution. The
+## elements of @var{p} must be probabilities
+## @end itemize
+## @var{n} and @var{p} 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 negative binomial distribution
+##
+## @item
+## @var{v} is the variance of the negative binomial distribution
+## @end itemize
+##
+## @subheading Examples
+##
+## @example
+## @group
+## n = 1:4;
+## p = 0.2:0.2:0.8;
+## [m, v] = nbinstat (n, p)
+## @end group
+##
+## @group
+## [m, v] = nbinstat (n, 0.5)
+## @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 negative binomial distribution
+
+function [m, v] = nbinstat (n, p)
+
+  # Check arguments
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  if (! isempty (n) && ! ismatrix (n))
+    error ("nbinstat: n must be a numeric matrix");
+  endif
+  if (! isempty (p) && ! ismatrix (p))
+    error ("nbinstat: p must be a numeric matrix");
+  endif
+
+  if (! isscalar (n) || ! isscalar (p))
+    [retval, n, p] = common_size (n, p);
+    if (retval > 0)
+      error ("nbinstat: n and p must be of common size or scalar");
+    endif
+  endif
+
+  # Calculate moments
+  q = 1 - p;
+  m = n .* q ./ p;
+  v = n .* q ./ (p .^ 2);
+
+  # Continue argument check
+  k = find (! (n > 0) | ! (n < Inf) | ! (p > 0) | ! (p < 1));
+  if (any (k))
+    m(k) = NaN;
+    v(k) = NaN;
+  endif
+
+endfunction
+
+%!test
+%! n = 1:4;
+%! p = 0.2:0.2:0.8;
+%! [m, v] = nbinstat (n, p);
+%! expected_m = [ 4.0000, 3.0000, 2.0000, 1.0000];
+%! expected_v = [20.0000, 7.5000, 3.3333, 1.2500];
+%! assert (m, expected_m, 0.001);
+%! assert (v, expected_v, 0.001);
+
+%!test
+%! n = 1:4;
+%! [m, v] = nbinstat (n, 0.5);
+%! expected_m = [1, 2, 3, 4];
+%! expected_v = [2, 4, 6, 8];
+%! assert (m, expected_m, 0.001);
+%! assert (v, expected_v, 0.001);