# pdfwak: Probability Density Function of the Wakeby Distribution In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

 pdfwak R Documentation

## Probability Density Function of the Wakeby Distribution

### Description

This function computes the probability density of the Wakeby distribution given parameters (ξ, α, β, γ, and δ) computed by `parwak`. The probability density function is

f(x) = (α[1-F(x)]^{β - 1} + γ[1-F(x)]^{-δ - 1})^{-1}\mbox{,}

where f(x) is the probability density for quantile x, F(x) is the cumulative distribution function or nonexceedance probability at x, ξ is a location parameter, α and β are scale parameters, and γ, and δ are shape parameters. The five returned parameters from `parwak` in order are ξ, α, β, γ, and δ.

### Usage

```pdfwak(x, para)
```

### Arguments

 `x` A real value vector. `para` The parameters from `parwak` or `vec2par`.

### Value

Probability density (f) for x.

W.H. Asquith

### References

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

Sourced from written communication with Dr. Hosking in October 2007.

`cdfwak`, `quawak`, `lmomwak`, `parwak`

### Examples

```## Not run:
lmr <- vec2lmom(c(1,0.5,.4,.3,.15))
wak <- parwak(lmr)
F <- nonexceeds()
x <- quawak(F,wak)
check.pdf(pdfwak,wak,plot=TRUE)

## End(Not run)
```

lmomco documentation built on Aug. 27, 2022, 1:06 a.m.