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

 Liouville_marginal R Documentation

## Liouville vectors marginal functions

### 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

``````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

``````## 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[1], theta=2)
su <- sliouvm(1-x[,1], family="gumbel", alpha=alphavec[1], 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 April 21, 2023, 9:07 a.m.