lmomgum {lmomco}R Documentation

L-moments of the Gumbel Distribution

Description

This function estimates the L-moments of the Gumbel distribution given the parameters (xi and α) from pargum. The L-moments in terms of the parameters are

λ_1 = xi + (0.5722...) α mbox{,}

λ_2 = α log(2) mbox{,}

tau_3 = 0.169925 mbox{,}

tau_4 = 0.150375 mbox{, and}

tau_5 = 0.055868 mbox{.}

Usage

lmomgum(para)

Arguments

para The parameters of the distribution.

Value

An R list is returned.

L1 Arithmetic mean.
L2 L-scale—analogous to standard deviation.
LCV coefficient of L-variation—analogous to coe. of variation.
TAU3 The third L-moment ratio or L-skew–analogous to skew.
TAU4 The fourth L-moment ratio or L-kurtosis—analogous to kurtosis.
TAU5 The fifth L-moment ratio.
L3 The third L-moment.
L4 The fourth L-moment.
L5 The fifth L-moment.
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, vol. 52, p. 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, quagum, cdfgum

Examples

lmr <- lmom.ub(c(123,34,4,654,37,78))
lmr
lmomgum(pargum(lmr))

[Package lmomco version 0.96.3 Index]