sicgbs {gbs}R Documentation

Schwartz information criterion for a sample from the GBSD

Description

The function sicgbs() gives the Schwartz information criterion (SIC) value assuming a GBSD with parameters α, βand a specific kernel.

Usage

sicgbs(x, nu = 1.0, kernel = "normal")

Arguments

x Vector of observations.
nu Shape parameter corresponding to the degrees of freedom of the t distribution. In the case of the Laplace, logistic, normal kernels, nu can be fixed at the value 1.0 since this parameter is not involved in these kernels.
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

The SIC is a selection model criterion based on information loss. According to this criterion, it is possible to choice a hypothetic model that better describe the data set considering the smaller SIC value. The SIC is defined as SIC = -l(theta)/n+ p log(n)/(2n), where l(theta) is the log-likelihood function associated with the model, n is the sample size and p is the number of involved parameters; for more details see Spieglhaiter et al. (2002).

Value

sicgbs() gives the value for the SIC of the GBSD.

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.

Spieglhaiter, D. J., Best, N. G., Carlin, B. P., van der Linde, A. (2002). Bayesian measures of complexity and fit. Journal of the Royal Statistical Society Series B 64, 1-34.

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 SIC value of the GBSD with normal kernel from the data x
sicgbs(x, nu = 1.0, kernel = "normal")

[Package gbs version 1.0 Index]