mleigSt {ig}R Documentation

MLE of the parameters of the IGTD generated from the t kernel

Description

The function mleigSt 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

mleigSt(x)

Arguments

x Vector of observations.

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 obtained by using an optimal methodology based on the data.

Value

mleigSt() 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.
nuOptimal Returns the optimal 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
mleigSt(x)

[Package ig version 1.2 Index]