L-moments of the Pearson Type III Distribution

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Description

This function estimates the L-moments of the Pearson Type III distribution given the parameters (μ, σ, and γ) 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.

Usage

1
lmompe3(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: “lmompe3”.

Author(s)

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.

See Also

parpe3, cdfpe3, pdfpe3, quape3

Examples

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lmr <- lmoms(c(123,34,4,654,37,78))
lmr
lmompe3(parpe3(lmr))

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