quagpa {lmomco}

Quantile Function of the Generalized Pareto Distribution

Description

This function computes the quantiles of the Generalized Pareto distribution given parameters (\xi, \alpha, and \kappa) computed by pargpa. The quantile function is

x(F) = \xi + \frac{\alpha}{\kappa} \left( 1-(1-F)^\kappa \right)\mbox{,}

for \kappa \ne 0, and

x(F) = \xi - \alpha\log(1-F)\mbox{,}

for \kappa = 0, where x(F) is the quantile for nonexceedance probability F, \xi is a location parameter, \alpha is a scale parameter, and \kappa is a shape parameter. The range of x is \xi \le x \le \xi + \alpha/\kappa if k > 0; \xi \le x < \infty if \kappa \le 0. Note that the shape parameter \kappa parameterization of the distribution herein follows that in tradition by the greater L-moment community and others use a sign reversal on \kappa. (The evd package is one example.)

Usage

quagpa(f, para, paracheck=TRUE)

Arguments

f

Nonexceedance probability (0 \le F \le 1).

para

The parameters from pargpa or vec2par.

paracheck

A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the quantile function in the context of TL-moments with nonzero trimming.

Value

Quantile value for nonexceedance probability F.

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

cdfgpa, pdfgpa, lmomgpa, pargpa

Examples

  lmr <- lmoms(c(123, 34, 4, 654, 37, 78))
  quagpa(0.5,pargpa(lmr))

## Not run: 
  # Let us compare L-moments, parameters, and 90th percentile for a simulated
  # GPA distibution of sample size 100 having the following parameters between
  # lmomco and lmom packages in R. The answers are the same.
  gpa.par <- lmomco::vec2par(c(1.02787, 4.54603, 0.07234), type="gpa")
  X <- lmomco::rlmomco(100, gpa.par)
   lmom::samlmu(X)
  lmomco::lmoms(X)
    lmom::pelgpa( lmom::samlmu(X))
  lmomco::pargpa(lmomco::lmoms(X))
    lmom::quagpa(0.90,   lmom::pelgpa(  lmom::samlmu(X)))
  lmomco::quagpa(0.90, lmomco::pargpa(lmomco::lmoms( X))) # 
## End(Not run)