lmom (version 3.2)

cdfwei: 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))

Value

cdfwei gives the distribution function;

quawei gives the quantile function.

Arguments

x

Vector of quantiles.

f

Vector of probabilities.

para

Numeric vector containing the parameters of the distribution, in the order \(\zeta, \beta, \delta\) (location, scale, shape).

Details

The Weibull distribution with location parameter \(\zeta\), scale parameter \(\beta\) and shape parameter \(\delta\) has distribution function $$F(x)=1-\exp[-\lbrace(x-\zeta)/\beta\rbrace^\delta]$$ for \(x>\zeta\).

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)