lmomTLgpa {lmomco}

Trimmed L-moments of the Generalized Pareto Distribution

Description

This function estimates the symmetrical trimmed L-moments (TL-moments) for t=1 of the Generalized Pareto distribution given the parameters (\xi, \alpha, and \kappa) from parTLgpa. The TL-moments in terms of the parameters are

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

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

\tau^{(1)}_3 = \frac{10(1-\kappa)}{9(\kappa+5)} \mbox{, and}

\tau^{(1)}_4 = \frac{5(\kappa-1)(\kappa-2)}{4(\kappa+6)(\kappa+5)} \mbox{.}

Usage

lmomTLgpa(para)

Arguments

para

The parameters of the distribution.

Value

An R list is returned.

lambdas

Vector of the trimmed L-moments. First element is \lambda^{(1)}_1, second element is \lambda^{(1)}_2, and so on.

ratios

Vector of the L-moment ratios. Second element is \tau^{(1)}, third element is \tau^{(1)}_3 and so on.

trim

Level of symmetrical trimming used in the computation, which is unity.

leftrim

Level of left-tail trimming used in the computation, which is unity.

rightrim

Level of right-tail trimming used in the computation, which is unity.

source

An attribute identifying the computational source of the TL-moments: “lmomTLgpa”.

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

lmomgpa, parTLgpa, cdfgpa, pdfgpa, quagpa

Examples

TL <- TLmoms(c(123,34,4,654,37,78,21,3400),trim=1)
TL
lmomTLgpa(parTLgpa(TL))