pdfgno {lmomco}R Documentation

Probability Density Function of the Generalized Normal Distribution

Description

This function computes the probability density of the Generalized Normal distribution given parameters (xi, α, and kappa) of the distribution computed by pargno. The probability density function function of the distribution is

f(x) = frac{exp{kappa y - y^2/2}}{α sqrt{2π}} mbox{,}

where Phi is the cumulative ditribution function of the standard normal distribution and y is

y = -kappa^{-1} log(1 - frac{kappa(x-xi)}{α}) mbox { for } kappa ne 0 mbox{, and}

y = (x-xi)/α mbox{ for } kappa = 0 mbox{,}

where f(x) is the probability density for quantile x, xi is a location parameter, α is a scale parameter, and kappa is a shape parameter.

Usage

pdfgno(x, para)

Arguments

x A real value.
para The parameters from pargno or similar.

Value

Probability density (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, vol. 52, p. 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

cdfgno, quagno, pargno

Examples

  lmr <- lmom.ub(c(123,34,4,654,37,78))
  gno <- pargno(lmr)
  x <- quagno(0.5,gno)
  pdfgno(x,gno)

[Package lmomco version 0.96.3 Index]