mleigStNuFixed {ig}R Documentation

MLE of the parameters of the IGT Student with fixed nu

Description

The function mleigStNuFixed gives the maximum likelihood estimates (MLE) of the parameters mu and lambda of the IGTD generated from the t kernel based on a sample of observations based on this distribution.

Usage

mleigStNuFixed(x, nu = 1)

Arguments

x Vector of observations.
nu Shape parameter corresponding to the degrees of freedom of the t distribution.

Details

The MLEs of the parameters mu and lambda of the classical IG distribution are obtained using the analytical expressions of these estimators. In the case of the IGTD generated from the t kernel, the MLEs of the parameters mu and lambda must be obtained using numerical procedure already implmented in R. In this procedure, the parameter nu is previosly fixed. This methodoly can be useful for simulation studies or to determine the optimal value of nu.

Value

mleigStNuFixed() computes MLEs for the parameters of the IGTD generated from the t kernel giving results according to the following list:

muEstimate Returns the value of the MLE of mu.
lambdaEstimate Returns the value of the MLE of lambda.
nuFixed Returns the fixed value for nu.
loglikelihood Returns the value of the IGTD loglikelihood.

Author(s)

Víctor Leiva <victor.leiva@uv.cl; victor.leiva@yahoo.com>,
Hugo Hernández <hugo.hernandez.p@gmail.com> and
Antonio Sanhueza <asanhueza@ufro.cl>.

References

Sanhueza, A., Leiva, V., Balakrishnan, N. (2008). A new class of inverse Gaussian type distributions. Metrika (in press).

Examples

## Generates a sample from the IGTD with t kernel
x <- rigt(300, mu = 1.0, lambda = 1.0, nu = 5, kernel = "t")

## Computes the likelihood for a sample x from the IGTD with t kernel
mleigStNuFixed(x, nu = 5)

[Package ig version 1.2 Index]