rcgbs {gbs}R Documentation

Relative change on the MLE of the GBSD

Description

The function rcgbs() computes the relative change (RC) on the MLE when some observations are removed in order to evaluate the effect of their potential influence.

Usage

rcgbs(x, casesRemoved = NULL, kernel = "normal")

Arguments

x Vector of observations.
casesRemoved Index of the potentially influential case(s) that must be removed.
kernel Kernel of the pdf of the associated symmetrical distribution by means of which the GBSD is obtained. The kernels: laplace, logistic, normal and t are available.

Details

This function computes the relative changes (RC), in percentage, of each estimated parameter, defined by mbox{RC}_{theta_j} = |(hat theta_j - hat theta_{j(mbox{tiny I})})/hat theta_j| times 100%, where hat theta_{j(mbox{tiny I})} denotes the MLE of theta_j after the set I of cases has been removed.

Value

rcgbs() gives the RCs on the MLEs of the parameters of the GBSD from a sample of observations without to consider some potentially influential case(s) related to the MLE of the complete sample.

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 RC the MLE of the parameters of the GBSD with g="normal" when the
##  case 1 has been removed
rcgbs(x, casesRemoved = c(1), kernel = "normal")

[Package gbs version 1.0 Index]