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


  • The cumulative distribution function is given by , where is the CDF for the kernel ker, and is the CDF for .
  • Marginal distribution can be any univariate distribution.
  • The following kernels ker can be used:
  • "Product"independent distributions
    "Maximal"FrechétHoeffding upper bound
    "Minimal"FrechétHoeffding lower bound
    {"Frank",α}Frank copula
    {"Clayton",c}ClaytonPareto copula
    {"GumbelHougaard",α}GumbelHougaard copula
    {"FGM",α}FarlieGumbelMorgenstern copula
    {"AMH",α}AliMikhailHaq copula
    {"Binormal",ρ}bivariate Gaussian with correlation
    {"Multinormal",Σ}multivariate Gaussian with covariance
    {"MultivariateT",Σ,ν}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.
Introduced in 2010
| Updated in 2014
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