Function File: p = copulapdf (family, x, theta)

Compute the probability density function of a copula family.

Arguments

• 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 -1 for the Clayton family, greater than or equal to 1 for the Gumbel-Hougaard family, arbitrary for the Frank family, and greater than or equal to -1 and lower than 1 for 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.

Return values

• p is the probability density of the copula at each row of x and corresponding parameter theta.

Examples

          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)

References

1. Roger B. Nelsen. An Introduction to Copulas. Springer, New York, second edition, 2006.