Description Usage Arguments Value Author(s) References See Also Examples
This function estimates the Lmoments 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 Lmoments 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 Lmoments, are in fact the product moments. Although, these values fitted by the method of Lmoments will not be numerically equal to the sample product moments. Further details are provided in the Examples section of the pmoms
function documentation.
1  lmompe3(para)

para 
The parameters of the distribution. 
An R list
is returned.
lambdas 
Vector of the Lmoments. First element is λ_1, second element is λ_2, and so on. 
ratios 
Vector of the Lmoment ratios. Second element is τ, third element is τ_3 and so on. 
trim 
Level of symmetrical trimming used in the computation, which is 
leftrim 
Level of lefttail trimming used in the computation, which is 
rightrim 
Level of righttail trimming used in the computation, which is 
source 
An attribute identifying the computational source of the Lmoments: “lmompe3”. 
W.H. Asquith
Hosking, J.R.M., 1990, Lmoments—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 Lmoments: 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 Lmoments: Cambridge University Press.
parpe3
, cdfpe3
, pdfpe3
, quape3
1 2 3 
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