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

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)

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.

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.

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 \(x \ge 0\).