lmomgum {lmomco}

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”.

Author(s)

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.

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))
lmomgum(pargum(lmr))