lmomco (version 2.2.5)

cdfgld: Cumulative Distribution Function of the Generalized Lambda Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Generalized Lambda distribution given parameters ($\xi$, $\alpha$, $\kappa$, 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

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 $x$.

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.

See Also

pdfgld, quagld, lmomgld, pargld

Examples

## 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)