mlegbs {gbs}R Documentation

MLE of the parameters of the GBSD

Description

The function mlegbs gives the maximum likelihood estimates (MLE) of the parameters α and β of the GBSD generated from the kernels: Laplace, logistic and normal (classical case) based on a sample of observations based on this distribution.

Usage

mlegbs(x, kernel = "normal")

Arguments

x Vector of observations.
kernel Kernel of the pdf of the associated symmetrical distribution by means of which the GBSD is obtained. The kernels: {"laplace"}, {"logistic"} and {"normal"} are available.

Details

The MLEs of the parameters α and β of the GBS distribution generated from the kernels: Laplace, logistic and normal, must be obtained using numerical procedure already implemented in R.

Value

{mlegbs()} computes MLEs for the parameters of the GBSD generated from the kernels: Laplace, logistic and normal 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.
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 = "normal")

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

[Package gbs version 1.0 Index]