cdfgld: Cumulative Distribution Function of the Generalized Lambda...

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) ```

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