Compute the probability density function of a copula family.
- family is the copula family name. Currently, family can be
'Clayton'for the Clayton family,
'Gumbel'for the Gumbel-Hougaard family,
'Frank'for the Frank family, or
'AMH'for the Ali-Mikhail-Haq family.
- x is the support where each row corresponds to an observation.
- theta is the parameter of the copula. The elements of theta must be greater than or equal to
-1for the Clayton family, greater than or equal to
1for the Gumbel-Hougaard family, arbitrary for the Frank family, and greater than or equal to
-1and lower than
1for the Ali-Mikhail-Haq family. Moreover, theta must be non-negative for dimensions greater than
2. theta must be a column vector with the same number of rows as x or be scalar.
- p is the probability density 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 = copulapdf ("Clayton", x, theta) p = copulapdf ("Gumbel", x, 2)
- Roger B. Nelsen. An Introduction to Copulas. Springer, New York, second edition, 2006.