Arguments

• 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. The last two are Octave extensions that MATLAB does not provide.
• 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 families it is the linear correlation matrix, and a scalar is expanded to a bivariate one. For the remaining families 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. The Farlie-Gumbel-Morgenstern family instead takes one parameter for every subset of the variables of order two or more, so theta is a row vector of length 2^d-d-1 or a matrix with one such row per observation; parameter sets violating the family’s linear constraints give NaN.
• df is the degrees of freedom of the Student’s t family, and is required by it. It must be a vector with the same number of rows as x or be scalar.

Return values

• y 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];
 y = copulapdf ("Clayton", x, theta)

 y = copulapdf ("Gumbel", x, 2)

References

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

Input arguments must be double or single; integer, logical, and character arrays are rejected. MATLAB accepts a character array and evaluates it at the character codes, which Octave deliberately does not, since a character array is an integer type and integers are refused too.

See also: copulacdf, copularnd

Source Code: copulapdf