Weibull {base}R Documentation

The Weibull Distribution

Description

Density, distribution function, quantile function and random generation for the Weibull distribution with parameters shape and scale.

Usage

dweibull(x, shape, scale = 1, log = FALSE)
pweibull(q, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
qweibull(p, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
rweibull(n, shape, scale = 1)

Arguments

x, q vector of quantiles.
p vector of probabilities.
n number of observations to generate.
shape, scale shape and scale parameters.
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 scale is omitted it assumes the default value of 1.

The Weibull distribution with shape parameter a and scale parameter b has density given by

f(x) = (a/b) (x/b)^(a-1) exp(- (x/b)^a)

for x > 0.

Value

dweibull gives the density, pweibull gives the distribution function, qweibull gives the quantile function, and rweibull generates random deviates.

See Also

dexp for the Exponential which is a special case of a Weibull distribution.

Examples

x <- 1:10
all.equal(dweibull(x, shape = 1), dexp(x))
all.equal(pweibull(x, shape = 1, scale = pi), pexp(x, rate = 1/pi))
all.equal(qweibull(x/11, shape = 1, scale = pi), qexp(x/11, rate = 1/pi))
[Package Contents]