lmomgev: L-moments of the Generalized Extreme Value Distribution

Description

This function estimates the L-moments of the Generalized Extreme Value distribution given the parameters ($\xi$, $\alpha$, and $\kappa$) from pargev. The L-moments in terms of the parameters are $$\lambda_1 = \xi + \frac{\alpha}{\kappa}(1-\Gamma(1+\kappa)) \mbox{,}$$ $$\lambda_2 = \frac{\alpha}{\kappa}(1-2^{-\kappa})\Gamma(1+\kappa) \mbox{,}$$ $$\tau_3 = \frac{2(1-3^{-\kappa})}{1-2^{-\kappa}} - 3 \mbox{, and}$$ $$\tau_4 = \frac{5(1-4^{-\kappa})-10(1-3^{-\kappa})+6(1-2^{-\kappa})}{1-2^{-\kappa}} \mbox{.}$$

Usage

lmomgev(para)

Value

An R

list is returned.

lambdas: Vector of the L-moments. First element is $\lambda_1$, second element is $\lambda_2$, and so on.
ratios: Vector of the L-moment ratios. Second element is $\tau$, third element is $\tau_3$ and so on.
trim: Level of symmetrical trimming used in the computation, which is 0.
leftrim: Level of left-tail trimming used in the computation, which is NULL.
rightrim: Level of right-tail trimming used in the computation, which is NULL.
source: An attribute identifying the computational source of the L-moments: “lmomgev”.

Arguments

para: The parameters of the distribution.

Author

W.H. Asquith

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, v. 52, pp. 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.