# lmomgno: L-moments of the Generalized Normal Distribution In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

 lmomgno R Documentation

## L-moments of the Generalized Normal Distribution

### Description

This function estimates the L-moments of the Generalized Normal (Log-Normal3) distribution given the parameters (ξ, α, and κ) from pargno. The L-moments in terms of the parameters are

λ_1 = ξ + \frac{α}{κ}(1-\mathrm{exp}(κ^2/2) \mbox{, and}

λ_2 = \frac{α}{κ}(\mathrm{exp}(κ^2/2)(1-2Φ(-κ/√{2})) \mbox{,}

where Φ is the cumulative distribution of the Standard Normal distribution. There are no simple expressions for τ_3, τ_4, and τ_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 λ_1, second element is λ_2, and so on. ratios Vector of the L-moment ratios. Second element is τ, third element is τ_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”.

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.

pargno, cdfgno, pdfgno, quagno, lmomln3
lmr <- lmoms(c(123,34,4,654,37,78))