% -*- texinfo -*-
% @deftypefn {Function File} {@var{p} =} copulacdf (@var{family}, @var{x}, @var{theta})
% @deftypefnx {Function File} {} copulacdf ('t', @var{x}, @var{theta}, @var{nu})
% Compute the cumulative distribution function of 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, @code{'Clayton'} for the Clayton family,
% @code{'Gumbel'} for the Gumbel-Hougaard family, @code{'Frank'} for
% the Frank family, @code{'AMH'} for the Ali-Mikhail-Haq family, or
% @code{'FGM'} for the Farlie-Gumbel-Morgenstern family.
%
% @item
% @var{x} is the support where each row corresponds to an observation.
%
% @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, the Gumbel-Hougaard family, the Frank family,
% and the Ali-Mikhail-Haq family, @var{theta} must be a vector with the
% same number of elements as observations in @var{x} or be scalar. For
% the Farlie-Gumbel-Morgenstern family, @var{theta} must be a matrix of
% coefficients for the Farlie-Gumbel-Morgenstern polynomial where each
% row corresponds to one set of coefficients for an observation in
% @var{x}. A single row is expanded. The coefficients are in binary
% order.
%
% @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
% observations in @var{x} or be scalar.
% @end itemize
%
% @subheading Return values
%
% @itemize @bullet
% @item
% @var{p} is the cumulative distribution 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 = copulacdf ('Clayton', x, theta)
% @end group
%
% @group
% x = [0.2:0.2:0.6; 0.2:0.1:0.4];
% theta = [0.2, 0.1, 0.1, 0.05];
% p = copulacdf ('FGM', x, theta)
% @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