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

## 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

 `1` ```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

 ```1 2 3 4 5 6 7 8``` ```## 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) ```

### Example output

```[1] "pdf function appears to integrate to unity"
\$isunity
[1] TRUE

\$F
[1] 0.998
```

lmomco documentation built on March 18, 2018, 1:45 p.m.