cdfgno {lmomco}

Cumulative Distribution Function of the Generalized Normal Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Generalized Normal distribution given parameters (\xi, \alpha, and \kappa) computed by pargno. The cumulative distribution function is

F(x) = \Phi(Y) \mbox{,}

where \Phi is the cumulative distribution function of the Standard Normal distribution and Y is

Y = -\kappa^{-1} \log\left(1 - \frac{\kappa(x-\xi)}{\alpha}\right)\mbox{,}

for \kappa \ne 0 and

Y = (x-\xi)/\alpha\mbox{,}

for \kappa = 0, where F(x) is the nonexceedance probability for quantile x, \xi is a location parameter, \alpha is a scale parameter, and \kappa is a shape parameter.

Usage

cdfgno(x, para)

Arguments

x

A real value vector.

para

The parameters from pargno or vec2par.

Value

Nonexceedance probability (F) for x.

Author(s)

W.H. Asquith

References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

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

See Also

pdfgno, quagno, lmomgno, pargno, cdfln3

Examples

  lmr <- lmoms(c(123,34,4,654,37,78))
  cdfgno(50,pargno(lmr))