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}] =} unidstat (@var{n})
18 ## Compute mean and variance of the discrete uniform distribution.
20 ## @subheading Arguments
24 ## @var{n} is the parameter of the discrete uniform distribution. The elements
25 ## of @var{n} must be positive natural numbers
28 ## @subheading Return values
32 ## @var{m} is the mean of the discrete uniform distribution
35 ## @var{v} is the variance of the discrete uniform distribution
38 ## @subheading Example
43 ## [m, v] = unidstat (n)
47 ## @subheading References
51 ## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics
52 ## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC,
56 ## Athanasios Papoulis. @cite{Probability, Random Variables, and Stochastic
57 ## Processes}. McGraw-Hill, New York, second edition, 1984.
61 ## Author: Arno Onken <asnelt@asnelt.org>
62 ## Description: Moments of the discrete uniform distribution
64 function [m, v] = unidstat (n)
71 if (! isempty (n) && ! ismatrix (n))
72 error ("unidstat: n must be a numeric matrix");
77 v = ((n .^ 2) - 1) ./ 12;
79 # Continue argument check
80 k = find (! (n > 0) | ! (n < Inf) | ! (n == round (n)));
90 %! [m, v] = unidstat (n);
91 %! expected_m = [1.0000, 1.5000, 2.0000, 2.5000, 3.0000, 3.5000];
92 %! expected_v = [0.0000, 0.2500, 0.6667, 1.2500, 2.0000, 2.9167];
93 %! assert (m, expected_m, 0.001);
94 %! assert (v, expected_v, 0.001);