X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fstatistics-1.1.3%2Fcopularnd.m;fp=octave_packages%2Fstatistics-1.1.3%2Fcopularnd.m;h=10033e0f614689080e64bd617c876dc545fee565;hp=0000000000000000000000000000000000000000;hb=f5f7a74bd8a4900f0b797da6783be80e11a68d86;hpb=1705066eceaaea976f010f669ce8e972f3734b05
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+## Copyright (C) 2012 Arno Onken
+##
+## 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 .
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{x} =} copularnd (@var{family}, @var{theta}, @var{n})
+## @deftypefnx {Function File} {} copularnd (@var{family}, @var{theta}, @var{n}, @var{d})
+## @deftypefnx {Function File} {} copularnd ('t', @var{theta}, @var{nu}, @var{n})
+## Generate random samples from a copula family.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @item
+## @var{family} is the copula family name. Currently, @var{family} can be
+## @code{'Gaussian'} for the Gaussian family, @code{'t'} for the Student's t
+## family, or @code{'Clayton'} for the Clayton family.
+##
+## @item
+## @var{theta} is the parameter of the copula. For the Gaussian and Student's t
+## copula, @var{theta} must be a correlation matrix. For bivariate copulas
+## @var{theta} can also be a correlation coefficient. For the Clayton family,
+## @var{theta} must be a vector with the same number of elements as samples to
+## be generated or be scalar.
+##
+## @item
+## @var{nu} is the degrees of freedom for the Student's t family. @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.
+##
+## @item
+## @var{d} is the number of columns of the matrix to be generated. @var{d} must
+## be a positive integer and corresponds to the dimension of the copula.
+## @end itemize
+##
+## @subheading Return values
+##
+## @itemize @bullet
+## @item
+## @var{x} is a matrix of random samples from the copula with @var{n} samples
+## of distribution dimension @var{d}.
+## @end itemize
+##
+## @subheading Examples
+##
+## @example
+## @group
+## theta = 0.5;
+## x = copularnd ("Gaussian", theta);
+## @end group
+##
+## @group
+## theta = 0.5;
+## nu = 2;
+## x = copularnd ("t", theta, nu);
+## @end group
+##
+## @group
+## theta = 0.5;
+## n = 2;
+## x = copularnd ("Clayton", theta, n);
+## @end group
+## @end example
+##
+## @subheading References
+##
+## @enumerate
+## @item
+## Roger B. Nelsen. @cite{An Introduction to Copulas}. Springer, New York,
+## second edition, 2006.
+## @end enumerate
+## @end deftypefn
+
+## Author: Arno Onken
+## Description: Random samples from a copula family
+
+function x = copularnd (family, theta, nu, n)
+
+ # Check arguments
+ if (nargin < 2)
+ print_usage ();
+ endif
+
+ if (! ischar (family))
+ error ("copularnd: family must be one of 'Gaussian', 't', and 'Clayton'");
+ endif
+
+ lower_family = lower (family);
+
+ # Check family and copula parameters
+ switch (lower_family)
+
+ case {"gaussian"}
+ # Gaussian family
+ if (isscalar (theta))
+ # Expand a scalar to a correlation matrix
+ theta = [1, theta; theta, 1];
+ endif
+ if (! ismatrix (theta) || any (diag (theta) != 1) || any (any (theta != theta')) || min (eig (theta)) <= 0)
+ error ("copularnd: theta must be a correlation matrix");
+ endif
+ if (nargin > 3)
+ d = n;
+ if (! isscalar (d) || d != size (theta, 1))
+ error ("copularnd: d must correspond to dimension of theta");
+ endif
+ else
+ d = size (theta, 1);
+ endif
+ if (nargin < 3)
+ n = 1;
+ else
+ n = nu;
+ if (! isscalar (n) || (n < 0) || round (n) != n)
+ error ("copularnd: n must be a non-negative integer");
+ endif
+ endif
+
+ case {"t"}
+ # Student's t family
+ if (nargin < 3)
+ print_usage ();
+ endif
+ if (isscalar (theta))
+ # Expand a scalar to a correlation matrix
+ theta = [1, theta; theta, 1];
+ endif
+ if (! ismatrix (theta) || any (diag (theta) != 1) || any (any (theta != theta')) || min (eig (theta)) <= 0)
+ error ("copularnd: theta must be a correlation matrix");
+ endif
+ if (! isscalar (nu) && (! isvector (nu) || length (nu) != n))
+ error ("copularnd: nu must be a vector with the same number of rows as x or be scalar");
+ endif
+ nu = nu(:);
+ if (nargin < 4)
+ n = 1;
+ else
+ if (! isscalar (n) || (n < 0) || round (n) != n)
+ error ("copularnd: n must be a non-negative integer");
+ endif
+ endif
+
+ case {"clayton"}
+ # Archimedian one parameter family
+ if (nargin < 4)
+ # Default is bivariate
+ d = 2;
+ else
+ d = n;
+ if (! isscalar (d) || (d < 2) || round (d) != d)
+ error ("copularnd: d must be an integer greater than 1");
+ endif
+ endif
+ if (nargin < 3)
+ # Default is one sample
+ n = 1;
+ else
+ n = nu;
+ if (! isscalar (n) || (n < 0) || round (n) != n)
+ error ("copularnd: n must be a non-negative integer");
+ endif
+ endif
+ if (! isvector (theta) || (! isscalar (theta) && size (theta, 1) != n))
+ error ("copularnd: theta must be a column vector with the number of rows equal to n or be scalar");
+ endif
+ if (n > 1 && isscalar (theta))
+ theta = repmat (theta, n, 1);
+ endif
+
+ otherwise
+ error ("copularnd: unknown copula family '%s'", family);
+
+ endswitch
+
+ if (n == 0)
+ # Input is empty
+ x = zeros (0, d);
+ else
+
+ # Draw random samples according to family
+ switch (lower_family)
+
+ case {"gaussian"}
+ # The Gaussian family
+ x = normcdf (mvnrnd (zeros (1, d), theta, n), 0, 1);
+ # No parameter bounds check
+ k = [];
+
+ case {"t"}
+ # The Student's t family
+ x = tcdf (mvtrnd (theta, nu, n), nu);
+ # No parameter bounds check
+ k = [];
+
+ case {"clayton"}
+ # The Clayton family
+ u = rand (n, d);
+ if (d == 2)
+ x = zeros (n, 2);
+ # Conditional distribution method for the bivariate case which also
+ # works for theta < 0
+ x(:, 1) = u(:, 1);
+ x(:, 2) = (1 + u(:, 1) .^ (-theta) .* (u(:, 2) .^ (-theta ./ (1 + theta)) - 1)) .^ (-1 ./ theta);
+ else
+ # Apply the algorithm by Marshall and Olkin:
+ # Frailty distribution for Clayton copula is gamma
+ y = randg (1 ./ theta, n, 1);
+ x = (1 - log (u) ./ repmat (y, 1, d)) .^ (-1 ./ repmat (theta, 1, d));
+ endif
+ k = find (theta == 0);
+ if (any (k))
+ # Produkt copula at columns k
+ x(k, :) = u(k, :);
+ endif
+ # Continue argument check
+ if (d == 2)
+ k = find (! (theta >= -1) | ! (theta < inf));
+ else
+ k = find (! (theta >= 0) | ! (theta < inf));
+ endif
+
+ endswitch
+
+ # Out of bounds parameters
+ if (any (k))
+ x(k, :) = NaN;
+ endif
+
+ endif
+
+endfunction
+
+%!test
+%! theta = 0.5;
+%! x = copularnd ("Gaussian", theta);
+%! assert (size (x), [1, 2]);
+%! assert (all ((x >= 0) & (x <= 1)));
+
+%!test
+%! theta = 0.5;
+%! nu = 2;
+%! x = copularnd ("t", theta, nu);
+%! assert (size (x), [1, 2]);
+%! assert (all ((x >= 0) & (x <= 1)));
+
+%!test
+%! theta = 0.5;
+%! x = copularnd ("Clayton", theta);
+%! assert (size (x), [1, 2]);
+%! assert (all ((x >= 0) & (x <= 1)));
+
+%!test
+%! theta = 0.5;
+%! n = 2;
+%! x = copularnd ("Clayton", theta, n);
+%! assert (size (x), [n, 2]);
+%! assert (all ((x >= 0) & (x <= 1)));
+
+%!test
+%! theta = [1; 2];
+%! n = 2;
+%! d = 3;
+%! x = copularnd ("Clayton", theta, n, d);
+%! assert (size (x), [n, d]);
+%! assert (all ((x >= 0) & (x <= 1)));