Density of the Extreme-Value Birnbaum-Saunders distribution

Probability density function of the EVBS distribution on the response (positive) scale. The EVBS variate \(T\) satisfies \(Z = (2/\alpha)\,\sinh\{(\log T - \eta)/2\} \sim \mathrm{GEV}(0,1,\gamma)\).

Usage

devbs(t, eta, alpha, gama, log = FALSE)

Arguments

t

Vector of positive quantiles.

eta

Location on the log scale, typically \(x^\top \beta\).

alpha

Positive shape (scale) parameter.

gama

Extreme-value shape parameter.

log

Logical; if TRUE, the log-density is returned.

Value

A numeric vector of (log-)density values.

Details

The extreme-value index of the response \(T\) is \(2\gamma\), not \(\gamma\). The transformation preserves the max-domain of attraction but doubles the tail index, because \(T \approx \beta\alpha^2 Z^2\) in the upper tail.

Examples

devbs(c(10, 20, 30), eta = 2.58, alpha = 0.19, gama = -0.16)
#> [1] 0.0385729564 0.0256715224 0.0002807054