LLOGIS3 {FAdist} | R Documentation |
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 .
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)