parTLgpa {lmomco}

Estimate the Parameters of the Generalized Pareto Distribution using Trimmed L-moments

Description

This function estimates the parameters of the Generalized Pareto distribution given the the trimmed L-moments (TL-moments) for t=1 of the data in TL-moment object with a trim level of unity (trim=1). The parameters are computed as

\kappa = \frac{10-45\tau^{(1)}_3}{9\tau^{(1)}_3+10} \mbox{,}

\alpha = \frac{1}{6}\lambda^{(1)}_2(\kappa+2)(\kappa+3)(\kappa+4) \mbox{, and}

\xi = \lambda^{(1)}_1 - \frac{\alpha(\kappa+5)}{(\kappa+2)(\kappa+3)} \mbox{.}

Usage

parTLgpa(lmom, ...)

Arguments

lmom

A TL-moment object created by TLmoms.

...

Other arguments to pass.

Value

An R list is returned.

type

The type of distribution: gpa.

para

The parameters of the distribution.

source

The source of the parameters: “parTLgpa”.

Author(s)

W.H. Asquith

References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, v. 43, pp. 299–314.

See Also

TLmoms, lmomTLgpa, cdfgpa, pdfgpa, quagpa

Examples

TL <- TLmoms(rnorm(20),trim=1)
parTLgpa(TL)