rfgbs {gbs} | R Documentation |
Reliability function (rf) for the GBSD with shape parameter alpha, scale parameter beta and associated kernel g.
rfgbs(x, alpha = 1.0, beta = 1.0, nu = 1.0, kernel = "normal")
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. |
The GBSD has rf given by
S_T(t) = 1- F_T(t); t >0.
rfgbs()
gives the rf of an GBSD.
Barros, Michelli <michelli.karinne@gmail.com>
Leiva, Victor <victor.leiva@uv.cl, victor.leiva@yahoo.com>
Paula, Gilberto A. <giapaula@ime.usp.br>
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.
## Computes the rf of the GBSD with normal kernel for a vector x with alpha = 1, ## beta = 1 x <- seq(0.01, 4, by = 0.01) rfx <- rfgbs(x, alpha = 1.0, beta = 1.0, nu = 1.0, kernel = "normal") print(rfx) ## At the end there is the graph of this pdf plot(x, rfx, main = "Rf of the GBSD (classical case)", ylab = "R(x)")