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

## Description

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

## Usage

 ```1 2``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## 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 May 30, 2017, 4:36 a.m.