lmom (version 1.1)

cdfwei: Weibull distribution

Description

Distribution function and quantile function of the Weibull distribution.

Usage

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

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).

Value

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

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.
quagev(runif(100), c(0,2,-0.5))

# 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)