lmomco (version 2.3.1)

cdfkap: Cumulative Distribution Function of the Kappa Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Kappa of the distribution computed by parkap. The cumulative distribution function is

$$F(x) = \left(1-h\left(1-\frac{\kappa(x-\xi)}{\alpha}\right)^{1/\kappa}\right)^{1/h} \mbox{,}$$

where \(F(x)\) is the nonexceedance probability for quantile \(x\), \(\xi\) is a location parameter, \(\alpha\) is a scale parameter, \(\kappa\) is a shape parameter, and \(h\) is another shape parameter.

Usage

cdfkap(x, para)

Arguments

x

A real value vector.

para

The parameters from parkap or vec2par.

Value

Nonexceedance probability (\(F\)) for \(x\).

References

Hosking, J.R.M., 1994, The four-parameter kappa distribution: IBM Journal of Reserach and Development, v. 38, no. 3, pp. 251--258.

Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.

See Also

pdfkap, quakap, lmomkap, parkap

Examples

# NOT RUN {
  lmr <- lmoms(c(123,34,4,654,37,78,21,32,231,23))
  cdfkap(50,parkap(lmr))
# }