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.
lmomgno(para)An R
list is returned.
Vector of the L-moments. First element is \(\lambda_1\), second element is \(\lambda_2\), and so on.
Vector of the L-moment ratios. Second element is \(\tau\), third element is \(\tau_3\) and so on.
Level of symmetrical trimming used in the computation, which is 0.
Level of left-tail trimming used in the computation, which is NULL.
Level of right-tail trimming used in the computation, which is NULL.
An attribute identifying the computational source of the L-moments: “lmomgno”.
The parameters of the distribution.
W.H. Asquith
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))
lmr
lmomgno(pargno(lmr))
Run the code above in your browser using DataLab