# cdfwei: Weibull distribution In lmom: L-Moments

 cdfwei R Documentation

## 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

 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.

### 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.

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)


lmom documentation built on Aug. 29, 2023, 9:07 a.m.