cdfgpa {lmomco} | R Documentation |
This function computes the cumulative probability or nonexceedance probability
of the Generalized Pareto distribution given parameters (xi, α, and kappa)
of the distribution computed
by pargpa
. The cumulative distribution function of the distribution is
F(x) = 1 - e^{-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 nonexceedance probability for quantile x, xi is a location parameter, α is a scale parameter, and kappa is a shape parameter.
cdfgpa(x, para)
x |
A real value. |
para |
The parameters from pargpa or similar. |
Nonexceedance probability (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)) cdfgpa(50,pargpa(lmr))