lmomco (version 2.2.4)

lmomgum: L-moments of the Gumbel Distribution

Description

This function estimates the L-moments of the Gumbel distribution given the parameters ($\xi$ and $\alpha$) from pargum. The L-moments in terms of the parameters are $\lambda_1 = [\xi + (0.5722\dots) \alpha]$, $\lambda_2 = \alpha \log(2)$, $\tau_3 = 0.169925$, $\tau_4 = 0.150375$, and $\tau_5 = 0.055868$.

Usage

lmomgum(para)

Arguments

para

The parameters of the distribution.

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: “lmomgum”.

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.

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

See Also

pargum, cdfgum, pdfgum, quagum

Examples

lmr <- lmoms(c(123,34,4,654,37,78))
lmr
lmomgum(pargum(lmr))