This function estimates the L-moments of the Generalized Logistic distribution given the parameters (\(\xi\), \(\alpha\), and \(\kappa\)) from parglo. The L-moments in terms of the parameters are
$$\lambda_1 = \xi + \alpha \left(\frac{1}{\kappa} - \frac{\pi}{\sin(\kappa\pi)}\right) \mbox{,}$$
$$\lambda_2 = \frac{\alpha \kappa \pi}{\sin(\kappa\pi)} \mbox{,}$$
$$\tau_3 = -\kappa \mbox{, and}$$
$$\tau_4 = \frac{(1+5\tau_3^2)}{6} = \frac{(1+5\kappa^2)}{6}\mbox{.}$$
lmomglo(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: “lmomglo”.
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.
parglo, cdfglo, pdfglo, quaglo
lmr <- lmoms(c(123,34,4,654,37,78))
lmr
lmomglo(parglo(lmr))
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