This function estimates the L-moments of the Pearson Type III distribution given the parameters (\(\mu\), \(\sigma\), and \(\gamma\)) from parpe3 as the product moments: mean, standard deviation, and skew. The first three L-moments in terms of these parameters are complex and numerical methods are required. For simplier expression of the distribution functions (cdfpe3, pdfpe3, and quape3) the “moment parameters” are expressed differently.
The Pearson Type III distribution is of considerable theoretical interest because the parameters, which are estimated via the L-moments, are in fact the product moments. Although, these values fitted by the method of L-moments will not be numerically equal to the sample product moments. Further details are provided in the Examples section of the pmoms function documentation.
lmompe3(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: “lmompe3”.
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.
parpe3, cdfpe3, pdfpe3, quape3
lmr <- lmoms(c(123,34,4,654,37,78))
lmr
lmompe3(parpe3(lmr))
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