frgbs {gbs}R Documentation

Failure rate of the GBSD

Description

Failure rate (fr) of the GBSD with shape parameter alpha, scale parameter beta and associated kernel g.

Usage

frgbs(x, alpha = 1.0, beta = 1.0, nu = 1.0, kernel = "normal")

Arguments

x Vector of observations.
alpha Shape parameter.
beta Scale parameter.
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 GBSD has hf given by

h_T(t) = frac{f_T(t)}{1-F_T(t)}

Value

{frgbs()} gives the fr 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.

Examples

## Computes the rf of the GBSD with normal kernel for a vector x with alpha = 1.0, 
## beta = 1.0
x  <- seq(0.01, 4, by = 0.01)
frx <- frgbs(x, alpha = 1.0, beta = 1.0, nu = 1.0, kernel = "normal")
print(frx)

## At the end there is the graph of this pdf
plot(x, frx, main = "fr of the GBSD (classical case)", ylab = "h(x)")

[Package gbs version 1.0 Index]