Weibull distribution

Description

Distribution function and quantile function of the Weibull distribution.

Usage

cdfwei(x, para = c(0, 1, 1))
quawei(f, para = c(0, 1, 1))

Arguments

Details

The Weibull distribution with location parameter zeta, scale parameter beta and shape parameter δ has distribution function

F(x) = 1 - exp[ - { (x - zeta) /beta }^delta ]

for x>zeta.

Value

cdfwei gives the distribution function; quawei gives the quantile function.

Note

The functions expect the distribution parameters in a vector, rather than as separate arguments as in the standard R distribution functions pnorm, qnorm, etc.

See Also

cdfgev for the generalized extreme-value distribution, of which the Weibull (reflected through the origin) is a special case.

Examples

# Random sample from a 2-parameter Weibull distribution
# with scale parameter 2 and shape parameter 1.5.
quawei(runif(100), c(0,2,1.5))

# Illustrate the relation between Weibull and GEV distributions.
# weifit() fits a Weibull distribution to data and returns
#   quantiles of the fitted distribution
# gevfit() fits a Weibull distribution as a "reverse GEV",
#   i.e. fits a GEV distribution to the negated data,
#   then computes negated quantiles
weifit <- function(qval, x) quawei(qval, pelwei(samlmu(x)))
gevfit <- function(qval, x) -quagev(1-qval, pelgev(samlmu(-x)))
# Compare on Ozone data
data(airquality)
weifit(c(0.2,0.5,0.8), airquality$Ozone)
gevfit(c(0.2,0.5,0.8), airquality$Ozone)

Results