pbs {bs}R Documentation

Cumulative distribution function (cdf) of the Birnbaum-Saunders distribution

Description

Cumulative distribution function of the BSD with shape parameter alpha and scale parameter beta.

Usage

pbs(q, alpha = 1, beta = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

q Vector of quantiles.
alpha Shape parameter.
beta Scale parameter.
lower.tail Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
log.p Logical; if TRUE, probabilities p are given as log(p).

Details

Birnbaum and Saunders (1969) proposed the two-parameter Birnbaum-Saunders distribution with density

f_{T}(t) = frac{1}{sqrt{2π}} exp<=ft[-frac{1}{2α^{2}} (frac{t}{β}+frac{β}{t}-2) right] frac{t^{-frac{3}{2}} (t+β)}{2αsqrt{β}}; t>0, α > 0, β > 0,

as a failure time distribution for fatigue failure caused under cyclic loading. The parameters alpha and beta are the shape and the scale parameters, respectively. In their derivation, it was assumed that the failure is due to the development and growth of a dominant crack.

Value

pbs() gives the cdf of an BSD.

Author(s)

Víctor Leiva <victor.leiva@uv.cl>, Hugo Hernández <hugo.hernande@msn.com>, and Marco Riquelme <mriquelm@ucm.cl>.

References

Birnbaum, Z. W. and Saunders, S. C. (1969). A new family of life distributions. J. Appl. Probab. 6(2): 637-652.

Examples

## Load package
library(bs)

## cdf for the Birnbaum-Saunders distribution
## with parameters alpha=0.5 y beta=1.0 in x=3.
pbs(3,alpha=0.5,beta=1.0,log=FALSE)

[Package bs version 1.0 Index]