# cdfwei: Weibull distribution In lmom: L-Moments

## Description

Distribution function and quantile function of the Weibull distribution.

## Usage

 ```1 2``` ```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 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.

`cdfgev` for the generalized extreme-value distribution, of which the Weibull (reflected through the origin) is a special case.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```# 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) ```