Random Number Generation from the EVBS Distribution

Generates random variates from the Extreme-Value Birnbaum-Saunders (EVBS) distribution by transforming Generalized Extreme Value (GEV) variates.

Usage

revbs(n, alpha, beta, gama)

Arguments

n: Sample size (number of variates to generate).
alpha: Shape parameter \(\alpha > 0\).
beta: Scale parameter \(\beta > 0\).
gama: Tail-shape parameter \(\gamma\) (real).

Value

A numeric vector of n EVBS variates. Returns NA if n is NA.

Details

If \(Z \sim \mathrm{GEV}(0, 1, \gamma)\), then \(T = \beta\{1 + \alpha^2 Z^2/2 + \alpha Z \sqrt{1 + \alpha^2 Z^2/4}\}\) follows the EVBS distribution. GEV variates are drawn by inversion, \(Z = (E^{-\gamma} - 1)/\gamma\) (or \(Z = -\log E\) when \(\gamma = 0\)) with \(E \sim\) Exp(1); for a given seed this reproduces exactly the variates of earlier versions, which used SpatialExtremes::rgev.

References

Ferreira, M., Gomes, M. I., and Leiva, V. (2012). On an extreme value version of the Birnbaum-Saunders distribution. REVSTAT, 10, 181–210.

Examples

set.seed(2023)
x <- revbs(100, alpha = 0.5, beta = 1, gama = 0.2)
summary(x)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>  0.5755  0.9404  1.3232  1.9947  1.9640 13.6259