cdfgpa {lmomco} | R Documentation |
Cumulative Distribution Function of the Generalized Pareto Distribution
Description
This function computes the cumulative probability or nonexceedance probability of the Generalized Pareto distribution given parameters (,
, and
) computed by
pargpa
. The cumulative distribution function is
where is
for and
for , where
is the nonexceedance probability for quantile
,
is a location parameter,
is a scale parameter, and
is a shape parameter. The range of
is
if
;
if
. Note that the shape parameter
parameterization of the distribution herein follows that in tradition by the greater L-moment community and others use a sign reversal on
. (The evd package is one example.)
Usage
cdfgpa(x, para)
Arguments
x |
A real value vector. |
para |
Value
Nonexceedance probability () for
.
Author(s)
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, doi:10.1111/j.2517-6161.1990.tb01775.x.
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.
See Also
pdfgpa
, quagpa
, lmomgpa
, pargpa
Examples
lmr <- lmoms(c(123, 34, 4, 654, 37, 78))
cdfgpa(50, pargpa(lmr))