lmomco (version 0.88)

lmomTLgpa: 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 TL-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
  Trim level = 1
• source
  An attribute identifying the computational source of the TL-moments: lmomTLgpa.

References

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

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. and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.

See Also

parTLgpa, quagpa, cdfgpa

Examples

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