FAdist (version 2.0)

WEIBULL3: Three-Parameter Weibull Distribution

Description

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

Usage

dweibull3(x,shape,scale=1,thres=0,log=FALSE)
pweibull3(q,shape,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE)
qweibull3(p,shape,scale=1,thres=0,lower.tail=TRUE,log.p=FALSE)
rweibull3(n,shape,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

• dweibull3 gives the density, pweibull3 gives the distribution function, qweibull3 gives the quantile function, and rweibull3 generates random deviates.

Details

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

See Also

dweibull, pweibull, qweibull, rweibull

Examples

m <- 100
x <- rweibull3(10,3,1,m)
dweibull3(x,3,1,m)
dweibull(x-m,3,1)