mlebs {gbs}R Documentation

Maximum likelihood estimation of the GBSD

Description

The function {mlebs} gives the maximum likelihood estimate (MLE) of the parameters α and β of the BSD (classical case) from a sample of observations based on this distribution.

Usage

mlebs(x)

Arguments

x Vector of observations.

Details

The MLEs of the parameters α and β of the classical IG distribution are obtained using the analytical expressions of these estimators.

Value

{mlebs()} computes MLEs for the parameters of the classical BSD 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.

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 normal kernel
x <- rgbs(300, alpha = 1.0, beta = 1.0,  nu = 1.0, kernel = "normal")

## Computes the likelihood for a sample x from the GBSD with normal kernel
mlebs(x)

[Package gbs version 1.0 Index]