lmomco (version 2.3.1)

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 {
# }
# 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)
# }