lmomgno: L-moments of the Generalized Normal Distribution

In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

L-moments of the Generalized Normal Distribution

Description

This function estimates the L-moments of the Generalized Normal (Log-Normal3) distribution given the parameters (\xi, \alpha, and \kappa) from pargno. The L-moments in terms of the parameters are

\lambda_1 = \xi + \frac{\alpha}{\kappa}(1-\mathrm{exp}(\kappa^2/2) \mbox{, and}

\lambda_2 = \frac{\alpha}{\kappa}(\mathrm{exp}(\kappa^2/2)(1-2\Phi(-\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. Logarthmic transformation of the data prior to fitting of the Generalized Normal distribution is not required. The distribution is algorithmically the same with subtle parameter modifications as the Log-Normal3 distribution (see lmomln3, parln3). If desired for user-level control of the lower bounds of a Log-Normal-like distribution is required, then see parln3.

Usage

lmomgno(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: “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, 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

pargno, cdfgno, pdfgno, quagno, lmomln3

Examples

lmr <- lmoms(c(123,34,4,654,37,78))
lmr
lmomgno(pargno(lmr))

lmomco documentation built on May 29, 2024, 10:06 a.m.