LLOGIS3 {FAdist}

Three-Parameter Log-Logistic Distribution

Description

Density, distribution function, quantile function and random generation for the 3-parameter log-logistic distribution with shape, scale, and threshold (or shift) parameters equal to shape, scale, and thres, respectively.

Usage

dllog3(x,shape=1,scale=1,thres=0,log=FALSE)
pllog3(q,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE)
qllog3(p,shape=1,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE)
rllog3(n,shape=1,scale=1,thres=0)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations.

shape

shape parameter.

scale

scale parameter.

thres

threshold (or shift) parameter.

log, log.p

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

lower.tail

logical; if TRUE (default), probabilities are P[X <= x],otherwise, P[X > x].

Details

If Y is a random variable distributed according to a logistic distribution (with location and scale parameters), then X = exp(Y)+m has a 3-parameter log-logistic distribution with shape and scale parameters corresponding to the scale and location parameteres of Y, respectively; and threshold parameter m.

Value

dllog3 gives the density, pllog3 gives the distribution function, qllog3 gives the quantile function, and rllog3 generates random deviates.

See Also

dlogis, plogis, qlogis, rlogis, dllog, pllog, qllog, rllog

Examples

m <- 100
x <- rllog3(10,1,0,m)
dllog3(x,1,0,m)
dllog(x-m,1,0)
dlogis(log(x-m),0,1)/(x-m)