| 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))