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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