# Liouville: Liouville copulas In lcopula: Liouville Copulas

## Description

Multivariate density, survival copula and random generation for the Liouville copulas.

## Usage

 ```1 2 3 4 5``` ```rliouv(n = 100, family, alphavec, theta, reverse = FALSE) pliouv(x, theta, family, alphavec) dliouv(x, family, alphavec, theta, is.log = FALSE) ```

## Arguments

 `n` sample size `family` family of the Liouville copula. Either `"clayton"`, `"gumbel"`, `"frank"`, `"AMH"` or `"joe"` `alphavec` vector of Dirichlet allocations (must be a vector of integers) Specifies (implictly) the dimension of sample `theta` parameter of the corresponding Archimedean copula `reverse` if `TRUE`, return sample from the corresponding survival copula `x` matrix of quantiles from a Liouville copula `is.log` if `TRUE`, will return the log-likelihood value

## Details

`rliouv` generates draws from the Liouville copula. `dliouv` evaluates the density of an `n` by `d` matrix of observations. `pliouv` is the (survival) copula associated with the Liouville vector and is as such the multivariate distribution function for uniform observations.

Liouville copulas were introduced in McNeil and Neslehova (2010), generalizing Archimedean copulas. Like the latter, they are survival copulas, which means that the copula is evaluated using the (multivariate) survival function of Liouville vectors. See also `sliouv` for the latter.

The Liouville copula is by definition a survival copula. The function thus maps marginally observations from the unit interval to the positive half-line using the marginal inverse survival function `isliouvm` of the Liouville vector, and then evaluating the survival distribution at the resulting Liouville vector.

## Value

either a matrix of dimension `n` by `length(alphavec)` with the corresponding quantile, probability, survival probability or sample from the Liouville vector

## References

McNeil A.J. and Neslehova, J.G. (2010) From Archimedean to Liouville Copulas. J. Multivar. Anal., 101(8): 1772–1790.

`Liouville_marginal`
 ```1 2 3 4 5 6 7 8 9``` ```## Not run: #Multivariate density of Clayton Liouville copula x <- rliouv(n = 100, family = "clayton", alphavec <- c(2,3), theta = 2) dliouv(x=x, family="clayton", alphavec=c(2,3), theta=2, TRUE) #Distribution function, multivariate sample x <- rliouv(n=100, family="frank", theta=1.5, alphavec=c(2,3)) pliouv(theta=1.5, x=x,family="frank", alphavec=c(2,3)) ## End(Not run) ```