Density, distribution function, quantile function, hazard function, cumulative hazard function, and random generation for the EV distribution with parameters shape and scale.

dEV(x, shape = 1, scale = 1, log = FALSE) 
pEV(q, shape = 1, scale = 1, lower.tail = TRUE, log.p = FALSE) 
qEV(p, shape = 1, scale = 1, lower.tail = TRUE, log.p = FALSE) 
hEV(x, shape = 1, scale = 1, log = FALSE) 
HEV(x, shape = 1, scale = 1, log.p = FALSE) 
rEV(n, shape = 1, scale = 1)

Arguments

shape, scale

shape and scale parameters, both defaulting to 1.

lower.tail

logical; if TRUE (default), probabilities are \(P(X \le x)\), otherwise, \(P(X > x)\).

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

Value

dEV gives the density, pEV gives the distribution function, qEV gives the quantile function, hEV gives the hazard function, HEV gives the cumulative hazard function, and rEV generates random deviates.

Invalid arguments will result in return value NaN, with a warning.

Details

The EV distribution with scale parameter \(a\) and shape parameter \(\sigma\) has hazard function given by $$h(x) = (b/\sigma)(x/\sigma)^(b-1)\exp((x / \sigma)^b)$$ for \(x \ge 0\).