FAdist (version 2.0)

LLOGIS3: 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]<="" em="">,otherwise, P[X > x].

Value

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

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 $m$.

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)