BS: The Classical Birnbaum-Saunders (BS) distribution

In santosneto/RBS: Regression models for Birnbaum-Saunders distributions

Description

Density, distribution function, quantile function and random generation for the normal distribution with mean equal to alpha and standard deviation equal to beta.

Usage

dcbs(x, alpha = 1, beta = 1, log = FALSE)

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

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

rcbs(n, alpha = 1, beta = 1)

Arguments

x, q	vector of quantiles
alpha	vector of scale parameter values
beta	vector of shape parameter values
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

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

f_{T}(t) = \frac{1}{√{2π}} \exp≤ft[-\frac{1}{2α^{2}} ≤ft(\frac{t}{β}+\frac{β}{t}-2\right) \right] \frac{t^{-\frac{3}{2}} (t+β)}{2α√{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

dcbs gives the density, pcbs gives the distribution function, qcbs gives the quantile function, and rcbs generates random deviates.

Author(s)

Víctor Leiva [e-mail], Hugo Hernández [e-mail], and Marco Riquelme [e-mail].

References

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

Chang D. S. and Tang, L. C. (1994). Random number generator for the Birnbaum-Saunders distribution. Computational and Industrial Engineering, 27(1-4):345-348.

Leiva, V., Sanhueza, A., Sen, P. K., and Paula, G. A. (2006). Random number generators for the generalized Birnbaum-Saunders distribution. Submitted to Publication.

Rieck, J. R. (2003). A comparison of two random number generators for the Birnbaum-Saunders distribution. Communications in Statistics - Theory and Methods, 32(5):929-934.

Examples

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

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

## quantil function for p=0.5 in the Birnbaum-Saunders distribution
qcbs(0.5,alpha=0.5,beta=1.0,log=FALSE)

## Examples for simulations
rcbs(n=6,alpha=0.5,beta=1.0)
sample<-rcbs(n=100,alpha=0.5,beta=1.0)
## Higtogram for sample
hist(sample)

santosneto/RBS documentation built on Feb. 5, 2021, 2:12 p.m.