lmomco: L-moments, Trimmed L-moments, L-comoments, 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. 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. This package is oriented around the FORTRAN algorithms of J.R.M. Hosking, and the nomenclature for many of the functions parallels that of the Hosking library. However, numerous extensions are made to aid in expand of the breadth and ease of L-moment application. Much theoretical extension of L-moment theory has occurred in recent years. E.A.H. Elamir and A.H. Seheult have developed the trimmed L-moments, which are implemented in this package. Further, recent developments by Robert Serfling and Peng Xiao have extended L-moments into multivariate space; the so-called sample L-comoments are implemented here. 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), Normal(L), Kappa(L), Pearson Type III(L), Reverse Gumbel(L[RC]), Wakeby(L), and Weibull(L).

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