# lmomco (1.7.3)

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

http://www.amazon.com/Distributional-Statistics-Environment-Statistical-Computing/dp/1463508417/

http://cran.r-project.org/web/packages/lmomco

The package implements the statistical theory of L-moments in R 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, and the method of L-moments can out perform the method of maximum likelihood. The lmomco package historically was originally oriented around canonical FORTRAN algorithms of Hosking's library, and the nomenclature for many of the functions parallels those of the Hosking library. Hosking's algorithms later became available in the lmom package. However, vast extensions, components, concepts, and other L-moment curiosities are added to lmomco to aid and expand the breadth of L-moment applications. Such extensions include venerable statistics as Sen weighted mean, Gini mean difference, plotting positions, and conditional probability adjustment. The plotting of L-moment ratio diagrams is directly supported in this package. Computations of L-moments for right-tail and left-tail censoring by known or unknown censoring threshold (Hosking) and also by indicator variable also are available. Trimmed L-moments are supported as is numerical integration of quantile functions to 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 so-called sample L-comoments are implemented and might have considerable application in copula theory because they measure asymmetric correlation 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 that uses only the sample L-skew and L-kurtosis. The package supports 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: 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).

**Maintainer**:
William Asquith

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

**License**: GPL

**Uses**: *Lmoments*, *copBasic*

**Reverse depends**: asbio, copBasic, SCI, SPEI

**Reverse suggests**: asbio, Lmoments, MGBT, TLMoments

Released almost 7 years ago.