BUILT-IN MATHEMATICA SYMBOL

represents a copula distribution with kernel distribution ker and marginal distributions , , ... .

## DetailsDetails

• The cumulative distribution function is given by , where is the CDF for the kernel ker, and is the CDF for .
• The following kernels ker can be used:
•  "Product" independent distributions "Maximal" Frechét-Hoeffding upper bound "Minimal" Frechét-Hoeffding lower bound {"Frank",} Frank copula {"Clayton",c} Clayton-Pareto copula {"GumbelHougaard",} Gumbel-Hougaard copula {"FGM",} Farlie-Gumbel-Morgenstern copula {"AMH",} Ali-Mikhail-Haq copula {"Binormal",} bivariate Gaussian with correlation {"Multinormal",} multivariate Gaussian with covariance {"MultivariateT",,} multivariate -distribution with scale matrix and degrees of freedom
• For , can be any positive number in two dimensions and any positive number less than or equal to 1 in higher dimensions.
• For , can be any positive number.
• For , can be any real number greater than or equal to 1.
• For and , can be any real number between and .
• The parameters for , , and are the same as for BinormalDistribution, MultinormalDistribution, and MultivariateTDistribution, respectively.
• CopulaDistribution can be used with such functions as Mean, PDF, and RandomVariate, etc.

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Define a product copula:

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Define a Farlie-Gumbel-Morgenstern copula:

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Define a three-dimensional maximal copula:

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