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copulapdf

PURPOSE ^

% Compute the probability density function of a copula family.

SYNOPSIS ^

function p = copulapdf (family, x, theta)

DESCRIPTION ^

% -*- texinfo -*-
% @deftypefn {Function File} {@var{p} =} copulapdf (@var{family}, @var{x}, @var{theta})
% Compute the probability density function of a copula family.
%
% @subheading Arguments
%
% @itemize @bullet
% @item
% @var{family} is the copula family name. Currently, @var{family} can
% be @code{'Clayton'} for the Clayton family, @code{'Gumbel'} for the
% Gumbel-Hougaard family, @code{'Frank'} for the Frank family, or
% @code{'AMH'} for the Ali-Mikhail-Haq family.
%
% @item
% @var{x} is the support where each row corresponds to an observation.
%
% @item
% @var{theta} is the parameter of the copula. The elements of
% @var{theta} must be greater than or equal to @code{-1} for the
% Clayton family, greater than or equal to @code{1} for the
% Gumbel-Hougaard family, arbitrary for the Frank family, and greater
% than or equal to @code{-1} and lower than @code{1} for the
% Ali-Mikhail-Haq family. Moreover, @var{theta} must be non-negative
% for dimensions greater than @code{2}. @var{theta} must be a column
% vector with the same number of rows as @var{x} or be scalar.
% @end itemize
%
% @subheading Return values
%
% @itemize @bullet
% @item
% @var{p} is the probability density of the copula at each row of
% @var{x} and corresponding parameter @var{theta}.
% @end itemize
%
% @subheading Examples
%
% @example
% @group
% x = [0.2:0.2:0.6; 0.2:0.2:0.6];
% theta = [1; 2];
% p = copulapdf ('Clayton', x, theta)
% @end group
%
% @group
% p = copulapdf ('Gumbel', x, 2)
% @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

CROSS-REFERENCE INFORMATION ^

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