mlebst {gbs}R Documentation

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

Description

The function {mlebst} gives the maximum likelihood estimates (MLE) of the parameters α and β of the GBSD generated from the t kernel based on a sample of observations based on this distribution.

Usage

mlebst(x)

Arguments

x Vector of observations.

Details

The MLEs of the parameters α and β of the GBSD generated from the t kernel must be obtained using numerical procedure already implemented in R. In this procedure, the parameter nu is obtained by using an optimal methodology based on the data.

Value

{mlebst()} computes MLEs for the parameters of the GBSD generated from the t kernel giving results according to the following list:

alphaEstimate Returns the value of the MLE of alpha.
betaEstimate Returns the value of the MLE of beta.
nuOptimal Returns the optimal value for nu.
loglikelihood Returns the value of the GBSD loglikelihood.

Author(s)

Barros, Michelli <michelli.karinne@gmail.com>
Leiva, Victor <victor.leiva@uv.cl, victor.leiva@yahoo.com>
Paula, Gilberto A. <giapaula@ime.usp.br>

References

Diaz-Garcia, J.A., Leiva, V. (2005) A new family of life distributions based on elliptically contoured distributions. J. Stat. Plan. Infer. 128:445-457 (Erratum: J. Stat. Plan. Infer. 137:1512-1513).

Leiva, V., Barros, M., Paula, G.A., Sanhueza, A. (2008) Generalized Birnbaum-Saunders distributions applied to air pollutant concentration. Environmetrics 19:235-249.

Sanhueza, A., Leiva, V., Balakrishnan, N. (2008) The generalized Birnbaum-Saunders distribution and its theory, methodology and application. Comm. Stat. Theory and Meth. 37:645-670.

Examples

## Generates a sample from the GBSD with t kernel
x <- rgbs(300, alpha = 1.0, beta = 1.0, nu = 5, kernel = "t")

## Computes the likelihood for a sample x from the GBSD with t kernel
mlebst(x)

[Package gbs version 1.0 Index]