Compute the cumulative distribution function of a copula family.
- family is the copula family name. Currently, family can be
'Gaussian'for the Gaussian family,
't'for the Student's t family,
'Clayton'for the Clayton family,
'Gumbel'for the Gumbel-Hougaard family,
'Frank'for the Frank family,
'AMH'for the Ali-Mikhail-Haq family, or
'FGM'for the Farlie-Gumbel-Morgenstern family.
- x is the support where each row corresponds to an observation.
- theta is the parameter of the copula. For the Gaussian and Student's t copula, theta must be a correlation matrix. For bivariate copulas theta can also be a correlation coefficient. For the Clayton family, the Gumbel-Hougaard family, the Frank family, and the Ali-Mikhail-Haq family, theta must be a vector with the same number of elements as observations in x or be scalar. For the Farlie-Gumbel-Morgenstern family, 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 x. A single row is expanded. The coefficients are in binary order.
- nu is the degrees of freedom for the Student's t family. nu must be a vector with the same number of elements as observations in x or be scalar.
- p is the cumulative distribution of the copula at each row of x and corresponding parameter theta.x = [0.2:0.2:0.6; 0.2:0.2:0.6]; theta = [1; 2]; p = copulacdf ("Clayton", x, theta) 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)
- Roger B. Nelsen. An Introduction to Copulas. Springer, New York, second edition, 2006.