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BUILT-IN MATHEMATICA SYMBOL
CopulaDistribution
CopulaDistribution[ker, {dist1, dist2, ...}]
represents a copula distribution with kernel distribution ker and marginal distributions 
, 
, ... .
Details
- 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.
New in 8
