| pdfgno {lmomco} | R Documentation |
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.
pdfgno(x, para)
x |
A real value. |
para |
The parameters from pargno or similar. |
Probability density (f) for x.
W.H. Asquith
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.
lmr <- lmom.ub(c(123,34,4,654,37,78)) gno <- pargno(lmr) x <- quagno(0.5,gno) pdfgno(x,gno)