# cdfgld: Cumulative Distribution Function of the Generalized Lambda... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

This function computes the cumulative probability or nonexceedance probability of the Generalized Lambda distribution given parameters (ξ, α, κ, and h) computed by `pargld`. The cumulative distribution function has no explicit form and requires numerical methods. The R function `uniroot` is used to root the quantile function `quagld` to compute the nonexceedance probability. The function returns 0 or 1 if the `x` argument is at or beyond the limits of the distribution as specified by the parameters.

## Usage

 `1` ```cdfgld(x, para, paracheck) ```

## Arguments

 `x` A real value vector. `para` The parameters from `pargld` or `vec2par`. `paracheck` A logical switch as to whether the validity of the parameters should be checked. Default is `paracheck=TRUE`. This switch is made so that the root solution needed for `cdfgld` exhibits an extreme speed increase because of the repeated calls to `quagld`.

## Value

Nonexceedance probability (F) for x.

W.H. Asquith

## References

Asquith, W.H., 2007, L-moments and TL-moments of the generalized lambda distribution: Computational Statistics and Data Analysis, v. 51, no. 9, pp. 4484–4496.

Karian, Z.A., and Dudewicz, E.J., 2000, Fitting statistical distributions—The generalized lambda distribution and generalized bootstrap methods: CRC Press, Boca Raton, FL, 438 p.

`pdfgld`, `quagld`, `lmomgld`, `pargld`

## Examples

 ```1 2 3 4 5 6 7 8``` ```## Not run: P <- vec2par(c(123,340,0.4,0.654),type='gld') cdfgld(300,P, paracheck=FALSE) par <- vec2par(c(0,-7.901925e+05, 6.871662e+01, -3.749302e-01), type="gld") supdist(par) ## End(Not run) ```

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