acigbs {gbs}R Documentation

Approximate confidence region for the parameters of the GBSD

Description

The function acigbs() produces a plot of an approximate confidence region and computes approximate confidence intervals (ACI) for the parameters α and β of the GBSD from a sample of observations.

Usage

  acigbs(x, kernel = "normal", confLevel = 95, 
         chart = c(NULL, NULL, NULL, NULL), 
         colourRegion = 1,
         colourEstimates = 2)

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, normal and t are available.
confLevel Confidence level of the region.
chart Vector of limits of the graphs. It is a vector of the type: c(xmin, xmax, ymin, ymax).
colourRegion Color of an approximate confidence region in the plot.
colourEstimates Color of MLE estimators in the plot.

Details

In order to construct a confidence region for α and β of the GBSD, we use the asymptotic normality of the MLEs.

Value

acigbs() shows a plot of an approximate confidence region and computes approximate confidence intervals (ACI) for the parameters of the GBSD considering the established confidence level from a sample of observatons giving results according to the following list:

alphaEstimate Return the value of the MLE of alpha.
alphaAci Return 95% ACI for alpha.
betaEstimate Return the value of the MLE of beta.
betaAci Return 95% ACI for 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")

## Estimates the parameters of the GBSD with normal kernel by means of a 
## 95% approximate confidence region and produces a graphical confidence 
## region
acigbs(x, kernel = "normal", confLevel = 95, colourRegion = 1, colourEstimates = 1)

[Package gbs version 1.0 Index]