| pdfgpa {lmomco} | R Documentation |
This function computes the probability density
of the Generalized Pareto distribution given parameters (xi, α, and kappa)
of the distribution computed
by pargpa. The probability density function of the distribution is
f(x) = α^{-1} e^{-(1-kappa)y} mbox{,}
where y is
y = -kappa^{-1} log(1 - frac{kappa(x-xi)}{α}) mbox{ for } kappa ne 0 mbox{, and}
y = (x-xi)/A 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.
pdfgpa(x, para)
x |
A real value. |
para |
The parameters from pargpa 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)) gpa <- pargpa(lmr) x <- quagpa(0.5,gpa) pdfgpa(x,gpa)