# liouv.maxim: Maximization of Liouville copula likelihood function In lcopula: Liouville Copulas

 liouv.maxim R Documentation

## Maximization of Liouville copula likelihood function

### Description

Two methods, either numerical optimization or method-of-moments

### Usage

``````liouv.maxim(
data,
family,
interval,
boundary = NULL,
lattice.mat = NULL,
return_all = FALSE,
MC.approx = TRUE
)
``````

### Arguments

 `data` sample matrix from a Liouville copula `family` family of the Liouville copula. Either `"clayton"`, `"gumbel"`, `"frank"`, `"AMH"` or `"joe"` `interval` interval over which to look for `theta` (bounds for Nelder-Mead) `boundary` vector of endpoints for search of Dirichlet allocation parameters. Either `boundary` or `lattice.mat` can be supplied `lattice.mat` matrix of tuples of Dirichlet allocation parameters at which to evaluate the likelihood `return_all` should all results (as list) or only maximum value be returned. Defaults to `FALSE` `MC.approx` whether to use Monte-Carlo approximation for the inverse survival function (default is `TRUE`)

### Details

A wrapper to `optim` using the Nelder-Mead algorithm or using the methods of moments, to maxime pointwise given every `alphavec` over a grid. Returns the maximum for `alphavec` and `theta`.

### Value

a list with values of `theta` and Dirichlet parameter along with maximum found. Gives index of maximum amongst models fitted.

### Examples

``````## Not run:
data <- rliouv(n=100, family="joe", alphavec=c(1,2), theta=2)
liouv.maxim(data=data, family="j", interval=c(1.25,3), boundary=c(2,2),return_all=TRUE)
lattice.mat <- t(combn(1:3,2))
liouv.maxim(data=data, family="j", interval=c(1.25,3), lattice.mat=lattice.mat, return_all=FALSE)
#data <- rliouv(n=1000, family="gumbel", alphavec=c(1,2), theta=2)
liouv.maxim.mm(data=data, family="gumbel", boundary=c(3,3),return_all=TRUE)
lattice.mat <- t(combn(1:3,2))
liouv.maxim.mm(data=data, family="gumbel", lattice.mat=lattice.mat, return_all=FALSE)

## End(Not run)
``````

lcopula documentation built on April 21, 2023, 9:07 a.m.