pdfgno: Probability Density Function of the Generalized Normal... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Description

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

f(x) = \frac{\exp(κ Y - Y^2/2)}{α √{2π}} \mbox{,}

where Y is

Y = -κ^{-1} \log≤ft(1 - \frac{κ(x-ξ)}{α}\right)\mbox{,}

for κ \ne 0, and

Y = (x-ξ)/α\mbox{,}

for κ = 0, where f(x) is the probability density for quantile x, ξ is a location parameter, α is a scale parameter, and κ is a shape parameter.

Usage

 1 pdfgno(x, para) 

Arguments

 x A real value vector. para The parameters from pargno or vec2par.

Value

Probability density (f) for x.

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.

cdfgno, quagno, lmomgno, pargno, pdfln3
 1 2 3 4  lmr <- lmoms(c(123,34,4,654,37,78)) gno <- pargno(lmr) x <- quagno(0.5,gno) pdfgno(x,gno)