lmomco (1.2.4)

L-moments, Trimmed L-moments, L-comoments, Censored L-moments, and Many Distributions.


The package implements the statistical theory of L-moments including L-moment estimation, probability-weighted moment estimation, parameter estimation for numerous familiar and not-so-familiar distributions, and L-moment estimation for the same distributions from the parameters. L-moments are derived from the expectations of order statistics and are linear with respect to the probability-weighted moments; choice of either can be made by mathematical convenience. L-moments are directly analogous to the well-known product moments; however, L-moments have many advantages including unbiasedness, robustness, and consistency with respect to the product moments. The method of L-moments can out perform the method of maximum likelihood. The lmomco package historically is oriented around canonical FORTRAN algorithms of J.R.M. Hosking, and the nomenclature for many of the functions parallels that of the Hosking library, which later became available in the lmom package. However, vast arrays of various extensions and curiosities are added by the author to aid and expand of the breadth of L-moment application. Such extensions include venerable statistics as Sen weighted mean, Gini mean difference, plotting positions, and conditional probability adjustment. Much extension of L-moment theory has occurred in recent years, including extension of L-moments into right-tail and left-tail censoring by known or unknown censoring threshold and also by indicator variable. E.A.H. Elamir and A.H. Seheult have developed the trimmed L-moments, which are implemented in this package. Further, Robert Serfling and Peng Xiao have extended L-moments into multivariate space; the so-called sample L-comoments are implemented here and might have considerable application in copula theory because they measure asymmetric correlation and higher co-moments. The supported distributions with moment type shown as L (L-moments) or TL (trimmed L-moments) and additional support for right-tail censoring ([RC]) include: Cauchy (TL), Exponential (L), Gamma (L), Generalized Extreme Value (L), Generalized Lambda (L & TL), Generalized Logistic (L), Generalized Normal (L), Generalized Pareto (L[RC] & TL), Gumbel (L), Kappa (L), Kumaraswamy (L), Normal (L), 3-parameter log-Normal (L), Pearson Type III (L), Rayleigh (L), Reverse Gumbel (L[RC]), Rice/Rician (L), Wakeby (L), and Weibull (L).

Maintainer: William Asquith
Author(s): William H. Asquith

License: GPL

Uses: Does not use any package
Reverse depends: asbio, copBasic, SCI, SPEI
Reverse suggests: asbio, Lmoments, MGBT, TLMoments

Released almost 9 years ago.