| 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
|
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.
Note
The cumulative hazard H(t) = - \log(1 - F(t))
is -pweibull(t, r, lower = FALSE, log = TRUE).
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))