# Liouville_marginal: Liouville vectors marginal functions In lcopula: Liouville Copulas

## Description

Marginal density, distribution, survival and inverse survival functions for Liouville copulas or Liouville vectors. The inverse survival function of Liouville vectors is not available in closed-form and is obtained numerically by root-finding. As such, Monte-Carlo approximation have been considered for dealing with inference to avoid computational bottlenecks. Note: the arguments of `sliouv` are reversed since they are meant to be called inside `optim`. The functions borrow psi functions and their derivatives from the `copula-package`.

## Usage

 ```1 2 3 4 5 6 7``` ```sliouvm(x, family, alpha, theta) pliouvm(x, family, alpha, theta) isliouvm(u, family, alpha, theta) dliouvm(x, family, alpha, theta) ```

## Arguments

 `x` vector of quantiles from a Liouville copula (or a Liouville vector for the survival function , with support on the positive real line) `family` family of the Liouville copula. Either `"clayton"`, `"gumbel"`, `"frank"`, `"AMH"` or `"joe"` `alpha` integer Dirichlet parameter `theta` parameter of the corresponding Archimedean copula `u` vector of quantiles or survival probabilities, (pseudo)-uniform variates

## Value

a vector with the corresponding quantile, probability, survival probabilities

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```## Not run: #Marginal density samp <- rliouv(n = 100, family = "clayton", alphavec <- c(2,3), theta = 2) dliouvm(x=samp[,1], family="clayton", alpha=2, theta=2) sum(log(dliouvm(x=samp[,1], family="clayton", alpha=2, theta=2))) #Marginal distribution and (inverse) survival function x <- rliouv(n = 100, family = "gumbel", alphavec <- c(2,3), theta = 2) pliouvm(x[,1], family="gumbel", alpha=alphavec, theta=2) su <- sliouvm(1-x[,1], family="gumbel", alpha=alphavec, theta=2) isliouvm(u=su, family="clayton", alpha=2, theta=2) #pliouv is the same as sliouv(isliouvm) ## End(Not run) ```

lcopula documentation built on July 7, 2019, 1:03 a.m.