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.)
quagpa(f, para, paracheck=TRUE)Quantile value for nonexceedance probability \(F\).
Nonexceedance probability (\(0 \le F \le 1\)).
The parameters from pargpa or vec2par.
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.
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, v. 52, pp. 105--124, tools:::Rd_expr_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.
cdfgpa, pdfgpa, lmomgpa, pargpa