Loglogistic: The Loglogistic Distribution

Description

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

Usage

dllogis(x, shape = 1, scale = 1, log = FALSE) 
pllogis(q, shape = 1, scale = 1, lower.tail = TRUE, log.p = FALSE) 
qllogis(p, shape = 1, scale = 1, lower.tail = TRUE, log.p = FALSE) 
hllogis(x, shape = 1, scale = 1, prop = 1, log = FALSE) 
Hllogis(x, shape = 1, scale = 1, prop = 1, log.p = FALSE) 
rllogis(n, shape = 1, scale = 1)

Value

dllogis gives the density, pllogis gives the distribution function, qllogis gives the quantile function, hllogis gives the hazard function, Hllogis gives the cumulative hazard function, and rllogis generates random deviates.

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

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).
prop: proportionality constant in the extended Loglogistic distribution.

Details

The Loglogistic 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 $x \ge 0$.