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}] =} betastat (@var{a}, @var{b})
18 ## Compute mean and variance of the beta distribution.
20 ## @subheading Arguments
24 ## @var{a} is the first parameter of the beta distribution. @var{a} must be
28 ## @var{b} is the second parameter of the beta distribution. @var{b} must be
31 ## @var{a} and @var{b} must be of common size or one of them must be scalar
33 ## @subheading Return values
37 ## @var{m} is the mean of the beta distribution
40 ## @var{v} is the variance of the beta distribution
43 ## @subheading Examples
49 ## [m, v] = betastat (a, b)
53 ## [m, v] = betastat (a, 1.5)
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 beta distribution
74 function [m, v] = betastat (a, b)
81 if (! isempty (a) && ! ismatrix (a))
82 error ("betastat: a must be a numeric matrix");
84 if (! isempty (b) && ! ismatrix (b))
85 error ("betastat: b must be a numeric matrix");
88 if (! isscalar (a) || ! isscalar (b))
89 [retval, a, b] = common_size (a, b);
91 error ("betastat: a and b must be of common size or scalar");
97 v = (a .* b) ./ (((a + b) .^ 2) .* (a + b + 1));
99 # Continue argument check
100 k = find (! (a > 0) | ! (a < Inf) | ! (b > 0) | ! (b < Inf));
111 %! [m, v] = betastat (a, b);
112 %! expected_m = [0.5000, 0.6250, 0.6818, 0.7143, 0.7353, 0.7500];
113 %! expected_v = [0.0833, 0.0558, 0.0402, 0.0309, 0.0250, 0.0208];
114 %! assert (m, expected_m, 0.001);
115 %! assert (v, expected_v, 0.001);
119 %! [m, v] = betastat (a, 1.5);
120 %! expected_m = [0.4000, 0.5714, 0.6667, 0.7273, 0.7692, 0.8000];
121 %! expected_v = [0.0686, 0.0544, 0.0404, 0.0305, 0.0237, 0.0188];
122 %! assert (m, expected_m, 0.001);
123 %! assert (v, expected_v, 0.001);