lmomco: L-moments, Censored L-moments, Trimmed L-moments, L-comoments,
and Many Distributions
The package provides a comparatively comprehensive implementation of the theory of L-moments. Implementations for L-moment and probability-weighted moment (PWM) estimation, and parameter estimation for numerous familiar and not-so-familiar distributions are provided. L-moment estimation for the same distributions from parameters. L-moments are linear functions of order statistics and are linearly related to PWMs. L-moments are analogous to product moments; however, L-moments have many advantages including unbiasedness, robustness, and consistency. L-moments can outperform maximum likelihood for small to moderate samples. The lmomco package historically was originally oriented around circa 1996-FORTRAN algorithms by Hosking, and the nomenclature parallels those of the Hosking library. The Hosking algorithms later became available in the lmom package. However, vast extensions, components, concepts, L-moment curiosities, and research topics are added to aid and expand the breadth of L-moment applications. Such extensions the Sen weighted mean, Gini mean difference, plotting positions, and conditional probability adjustments. L-moment ratio diagrams are supported. Computations of L-moments for right-tail and left-tail censoring by known or unknown censoring threshold (via Hosking) and also by indicator variable (via Wang et al.) also are available. Asymmetric trimmed L-moments are supported as are numerical integration dynamically compute trajectories of select TL-moment ratios for the construction of TL-moment ratio diagrams. L-moments have been extended into multivariate space; the sample L-comoments are implemented and might have considerable application in copula theory because L-comoments measure asymmetric association and higher comoments or comovements of variables. The package supports exact analytical boot-strap estimates of order statistics, L-moments, and variances-covariances of L-moments. The package provides the Harri-Coble Tau34-squared Test for Normality using sample L-skew and L-kurtosis. Support for the following distributions, with moment type shown as "L" (L-moments) or "TL" (trimmed L-moments) and additional support for right-tail censoring ([RC]) include, is available: Asymmetric Exponential Power (L), Cauchy (TL), Eta-Mu (L), 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), Kappa-Mu (L), Kumaraswamy (L), Laplace (L), Normal (L), 3-parameter log-Normal (L), Pearson Type III (L), Rayleigh (L), Reverse Gumbel (L[RC]), Rice/Rician (L), Truncated Exponential (L), Wakeby (L), and Weibull (L).