1 ## Copyright (C) 2006, 2007 Arno Onken <asnelt@asnelt.org>
3 ## This program is free software; you can redistribute it and/or modify it under
4 ## the terms of the GNU General Public License as published by the Free Software
5 ## Foundation; either version 3 of the License, or (at your option) any later
8 ## This program is distributed in the hope that it will be useful, but WITHOUT
9 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
10 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
13 ## You should have received a copy of the GNU General Public License along with
14 ## this program; if not, see <http://www.gnu.org/licenses/>.
17 ## @deftypefn {Function File} {[@var{m}, @var{v}] =} nbinstat (@var{n}, @var{p})
18 ## Compute mean and variance of the negative binomial distribution.
20 ## @subheading Arguments
24 ## @var{n} is the first parameter of the negative binomial distribution. The elements
25 ## of @var{n} must be natural numbers
28 ## @var{p} is the second parameter of the negative binomial distribution. The
29 ## elements of @var{p} must be probabilities
31 ## @var{n} and @var{p} must be of common size or one of them must be scalar
33 ## @subheading Return values
37 ## @var{m} is the mean of the negative binomial distribution
40 ## @var{v} is the variance of the negative binomial distribution
43 ## @subheading Examples
49 ## [m, v] = nbinstat (n, p)
53 ## [m, v] = nbinstat (n, 0.5)
57 ## @subheading References
61 ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics
62 ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC,
66 ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic
67 ## Processes}. McGraw-Hill, New York, second edition, 1984.
71 ## Author: Arno Onken <asnelt@asnelt.org>
72 ## Description: Moments of the negative binomial distribution
74 function [m, v] = nbinstat (n, p)
81 if (! isempty (n) && ! ismatrix (n))
82 error ("nbinstat: n must be a numeric matrix");
84 if (! isempty (p) && ! ismatrix (p))
85 error ("nbinstat: p must be a numeric matrix");
88 if (! isscalar (n) || ! isscalar (p))
89 [retval, n, p] = common_size (n, p);
91 error ("nbinstat: n and p must be of common size or scalar");
98 v = n .* q ./ (p .^ 2);
100 # Continue argument check
101 k = find (! (n > 0) | ! (n < Inf) | ! (p > 0) | ! (p < 1));
112 %! [m, v] = nbinstat (n, p);
113 %! expected_m = [ 4.0000, 3.0000, 2.0000, 1.0000];
114 %! expected_v = [20.0000, 7.5000, 3.3333, 1.2500];
115 %! assert (m, expected_m, 0.001);
116 %! assert (v, expected_v, 0.001);
120 %! [m, v] = nbinstat (n, 0.5);
121 %! expected_m = [1, 2, 3, 4];
122 %! expected_v = [2, 4, 6, 8];
123 %! assert (m, expected_m, 0.001);
124 %! assert (v, expected_v, 0.001);