lmomgno {lmomco}R Documentation

L-moments of the Generalized Normal Distribution

Description

This function estimates the L-moments of the Generalized Normal (log-Normal) distribution given the parameters (xi, α, and kappa) from pargno. The L-moments in terms of the parameters are

λ_1 = xi + frac{α}{kappa}(1-e^{kappa^2/2}) mbox{ and}

λ_2 = frac{α}{kappa}(e^{kappa^2/2})(1-2Phi(-kappa/sqrt{2})) mbox{,}

where Phi is the cumulative distribution of the standard normal distribution. There are no simple expressions for tau_3, tau_4, and tau_5. Log transformation of the data prior to fitting of the Generalized Normal distribution is not required.

Usage

lmomgno(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: “lmomgno”.

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

pargno, quagno, cdfgno

Examples

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

[Package lmomco version 0.96.3 Index]