lmomco (version 2.4.14)

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

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

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)

Value

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

Arguments

x

A real value vector.

para

The parameters from parkap or vec2par.

Author

W.H. Asquith

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

  lmr <- lmoms(c(123,34,4,654,37,78,21,32,231,23))
  cdfkap(50,parkap(lmr))