lmomco (version 2.4.14)

pdfgno: Probability Density Function of the Generalized Normal Distribution

Description

This function computes the probability density of the Generalized Normal distribution given parameters (\(\xi\), \(\alpha\), and \(\kappa\)) computed by pargno. The probability density function function is $$f(x) = \frac{\exp(\kappa Y - Y^2/2)}{\alpha \sqrt{2\pi}} \mbox{,} $$ where \(Y\) 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 probability density for quantile \(x\), \(\xi\) is a location parameter, \(\alpha\) is a scale parameter, and \(\kappa\) is a shape parameter.

Usage

pdfgno(x, para)

Value

Probability density (\(f\)) for \(x\).

Arguments

x

A real value vector.

para

The parameters from pargno or vec2par.

Author

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

cdfgno, quagno, lmomgno, pargno, pdfln3

Examples

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