/usr/share/octave/packages/statistics-1.3.0/mvtrnd.m is in octave-statistics 1.3.0-4.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 | ## Copyright (C) 2012 Arno Onken <asnelt@asnelt.org>, Iñigo Urteaga
##
## 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{x} =} mvtrnd (@var{sigma}, @var{nu})
## @deftypefnx {Function File} {@var{x} =} mvtrnd (@var{sigma}, @var{nu}, @var{n})
## Generate random samples from the multivariate t-distribution.
##
## @subheading Arguments
##
## @itemize @bullet
## @item
## @var{sigma} is the matrix of correlation coefficients. If there are any
## non-unit diagonal elements then @var{sigma} will be normalized, so that the
## resulting covariance of the obtained samples @var{x} follows:
## @code{cov (x) = nu/(nu-2) * sigma ./ (sqrt (diag (sigma) * diag (sigma)))}.
## In order to obtain samples distributed according to a standard multivariate
## t-distribution, @var{sigma} must be equal to the identity matrix. To generate
## multivariate t-distribution samples @var{x} with arbitrary covariance matrix
## @var{sigma}, the following scaling might be used:
## @code{x = mvtrnd (sigma, nu, n) * diag (sqrt (diag (sigma)))}.
##
## @item
## @var{nu} is the degrees of freedom for the multivariate t-distribution.
## @var{nu} must be a vector with the same number of elements as samples to be
## generated or be scalar.
##
## @item
## @var{n} is the number of rows of the matrix to be generated. @var{n} must be
## a non-negative integer and corresponds to the number of samples to be
## generated.
## @end itemize
##
## @subheading Return values
##
## @itemize @bullet
## @item
## @var{x} is a matrix of random samples from the multivariate t-distribution
## with @var{n} row samples.
## @end itemize
##
## @subheading Examples
##
## @example
## @group
## sigma = [1, 0.5; 0.5, 1];
## nu = 3;
## n = 10;
## x = mvtrnd (sigma, nu, n);
## @end group
##
## @group
## sigma = [1, 0.5; 0.5, 1];
## nu = [2; 3];
## n = 2;
## x = mvtrnd (sigma, nu, 2);
## @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
## Samuel Kotz and Saralees Nadarajah. @cite{Multivariate t Distributions and
## Their Applications}. Cambridge University Press, Cambridge, 2004.
## @end enumerate
## @end deftypefn
## Author: Arno Onken <asnelt@asnelt.org>
## Description: Random samples from the multivariate t-distribution
function x = mvtrnd (sigma, nu, n)
# Check arguments
if (nargin < 2)
print_usage ();
endif
if (! ismatrix (sigma) || any (any (sigma != sigma')) || min (eig (sigma)) <= 0)
error ("mvtrnd: sigma must be a positive definite matrix");
endif
if (!isvector (nu) || any (nu <= 0))
error ("mvtrnd: nu must be a positive scalar or vector");
endif
nu = nu(:);
if (nargin > 2)
if (! isscalar (n) || n < 0 | round (n) != n)
error ("mvtrnd: n must be a non-negative integer")
endif
if (isscalar (nu))
nu = nu * ones (n, 1);
else
if (length (nu) != n)
error ("mvtrnd: n must match the length of nu")
endif
endif
else
n = length (nu);
endif
# Normalize sigma
if (any (diag (sigma) != 1))
sigma = sigma ./ sqrt (diag (sigma) * diag (sigma)');
endif
# Dimension
d = size (sigma, 1);
# Draw samples
y = mvnrnd (zeros (1, d), sigma, n);
u = repmat (chi2rnd (nu), 1, d);
x = y .* sqrt (repmat (nu, 1, d) ./ u);
endfunction
%!test
%! sigma = [1, 0.5; 0.5, 1];
%! nu = 3;
%! n = 10;
%! x = mvtrnd (sigma, nu, n);
%! assert (size (x), [10, 2]);
%!test
%! sigma = [1, 0.5; 0.5, 1];
%! nu = [2; 3];
%! n = 2;
%! x = mvtrnd (sigma, nu, 2);
%! assert (size (x), [2, 2]);
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