rbs {bs}R Documentation

Random number generator from the Birnbaum-Saunders distribution

Description

Generate random numbers from the BSD with shape parameter alpha and scale parameter beta. The function rbs() selects the most appropriate method automatically. For details about effectiveness and efficiency of these three generators and the way to select the most suitable one see Leiva et al. (2006).

Usage

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

Arguments

n Number of observations.
alpha Shape parameter.
beta Scale parameter.

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 bata 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

rbs() gives a vector of n random numbers from the BSD with specific values of alpha and beta.

Author(s)

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

References

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

## Examples for simulations
rbs1(n=6,alpha=0.5,beta=1.0)
rbs2(n=6,alpha=0.5,beta=1.0)
rbs3(n=6,alpha=0.5,beta=1.0)

rbs(n=6,alpha=0.5,beta=1.0)

sample<-rbs(n=100,alpha=0.5,beta=1.0)
## Higtogram for sample
hist(sample)

[Package bs version 1.0 Index]