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, 'Frank' for the Frank family, 'Gumbel' for the Gumbel-Hougaard 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. Every family but Clayton is generated as bivariate only.
• 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, Frank and Gumbel-Hougaard families, theta must be a vector with the same number of elements as samples to be generated or be scalar. Values outside a family’s range give NaN rows: at or above 1 for the Gumbel-Hougaard family, at or above -1 for the bivariate Clayton family, and any finite value for the Frank family. The Ali-Mikhail-Haq family takes theta in [-1, 1) and the Farlie-Gumbel-Morgenstern family in [-1, 1].
• df is the degrees of freedom for the Student’s t family. df must be a vector with the same number of elements as samples to be generated or be scalar.
• n is the number of rows of the matrix to be generated. n must be a non-negative integer and corresponds to the number of samples to be generated.
• d is the number of columns of the matrix to be generated. d must be a positive integer and corresponds to the dimension of the copula.

Return values

• r is a matrix of random samples from the copula with n samples of distribution dimension d.

Examples

 theta = 0.5;
 r = copularnd ("Gaussian", theta);

 theta = 0.5;
 df = 2;
 r = copularnd ("t", theta, df);

 theta = 0.5;
 n = 2;
 r = copularnd ("Clayton", theta, n);

References

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

Source Code: copularnd