Define a product copula using two normal distributions:
Probability density function:
Cumulative distribution function:
Define a Frank copula using two uniform distributions:
Generate random vectors:
Compare means and variances:
Define an FGM copula with beta distributions:
Moment and moment-generating function:
Define a maximal copula with discrete components:
Probability density function:
Compute probabilities and expectations:
Define a minimal copula with Poisson distributions:
Probability density function:
Statistical properties are calculated componentwise:
Estimate distribution parameters:
A product copula:
Probability density function:
Cumulative distribution function:
A maximal copula:
Cumulative distribution function:
A minimal copula:
Cumulative distribution function:
A Frank copula:
Probability density function:
Cumulative distribution function:
A Clayton copula:
Probability density function:
Cumulative distribution function:
A Gumbel-Hougaard copula:
Probability density function:
Cumulative distribution function:
A Farlie-Gordon-Morgenstern copula:
Probability density function:
Cumulative distribution function:
An Ali-Mikhail-Haque copula:
Probability density function:
Cumulative distribution function:
A binormal copula:
Probability density function:
A multinormal copula:
Probability density function:
A multivariate Student
copula:
Probability density function:
Define a minimal copula with beta distributions as marginals:
Cumulative distribution function:
Survival function:
Define a maximal copula with different continuous marginals:
Cumulative distribution function:
Mean and variance:
Skewness and kurtosis:
Define a copula with Poisson marginal distributions:
Probability density function:
Hazard function:
Define a copula with negative binomial distribution marginals:
Probability density function:
Generate random numbers:
Probability density function:
Mean and variance:
Define a copula with
EmpiricalDistribution:
Probability density function:
Define a copula with a
HistogramDistribution:
Plot probability density function:
Cumulative distribution function:
Define a copula distribution with a
TruncatedDistribution as a marginal:
Probability density function:
Define a copula distribution with a
CensoredDistribution as a marginal:
Probability density function:
Mean and variance:
Define a copula with a
MixtureDistribution as a marginal:
Probability density function:
Cumulative distribution function:
Define a copula with a
ParameterMixtureDistribution as a marginal:
Probability density function:
Hazard function:
Define a copula with an
OrderDistribution as a marginal:
Probability density function:
Cumulative distribution function:
Define a copula with a
TransformedDistribution as a marginal:
Probability density function:
Mean and variance:
Skewness and kurtosis:
Define a copula with a
MarginalDistribution as a marginal:
Probability density function:
, 
, ....
, where 
is the CDF for the kernel ker, and 
is the CDF for 
.
}
}
}
}
-distribution with scale matrix 
and 
degrees of freedom
, 
can be any positive number.
, 
can be any positive number.
, 
can be any real number greater than or equal to 1.
and 
, 
can be any real number between 
and 
.
, 
, and 
are the same as for BinormalDistribution, MultinormalDistribution, and MultivariateTDistribution, respectively.
. Dependencies in the time to failure are modeled by Farlie-Gumbel-Morgenstern copula with 
. Find the probability that no component fails before 500 hours: 
and 
and volatilities 
and 
, respectively. Assuming both initial values to be 1, find the bounds for the joint cumulative distribution function of both assets at time 
:
and 
and initial assets both equal to 1. Assume the values of the assets follow a geometric Brownian motion with drifts 
and 
and volatilities 
and 
, respectively. Find the joint probability of the default at time 
assuming a Frank copula:
copula with one degree of freedom:
copula with normal marginals is a MultivariateTDistribution:
EXAMPLES
Basic Examples 
Scope 