lmomco (version 0.88)

quagpa: Quantile Function of the Generalized Pareto Distribution

Description

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

$$x(F) = \xi + \frac{\alpha}{\kappa} \left( 1-(1-F)^\kappa \right) \mbox{ for } \kappa \ne 0 \mbox{ and }$$

$$x(F) = \xi - \alpha\log(1-F) \mbox{ for } \kappa = 0 \mbox{,}$$

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.

Usage

quagpa(f, para)

Arguments

f

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

para

The parameters from pargpa or similar.

Value

• Quantile value for nonexceedance probability $F$.

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, 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.

See Also

cdfgpa, pargpa

Examples

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