L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments,
and Many Distributions
Description
Extensive functions for the theory of L-moments (LMs) in addition to probability-weighted moments (PWMs), and parameter (p) estimation for numerous familiar and not-so-familiar distributions. Estimation of LMs for the same distributions is provided as are L-moment ratio diagrams. Estimation of LMs for right-tail and left-tail censoring by known or unknown threshold and also by indicator variable is available. Asymmetric trimmed LMs (TL-moments, TLMs) are supported as are numerical integrations to dynamically compute trajectories of select TLM ratios for TL-moment ratio diagram construction. LMs of residual (resid.) and reversed (rev.) resid. life are implemented along with 13 operators on quantile functions that are useful in reliability, lifetime, and survival analysis. Exact analytical bootstrap estimates of order statistics, LMs, and variances-covariances of LMs are provided. The Harri-Coble Tau34-squared Test for Normality is available. Distribution support with "L" (LMs), "TL" (TLMs) and added (+) support for right-tail censoring (RC) encompasses: Asymmetric (Asy.) Exponential (Exp.) Power [L], Asy. Triangular [L], Cauchy [TL], Eta-Mu [L], Exp. [L], Gamma [L], Generalized (Gen.) Exp. Poisson [L], Gen. Extreme Value [L], Gen. Lambda [L,TL], Gen. Logistic [L), Gen. Normal [L], Gen. Pareto [L+RC, TL], Govindarajulu [L], Gumbel [L], Kappa [L], Kappa-Mu [L], Kumaraswamy [L], Laplace [L], Linear Mean Residual Quantile Function [L], Normal [L], 3-p log-Normal [L], Pearson Type III [L], Rayleigh [L], Rev. Gumbel [L+RC], Rice/Rician (L), Slash [TL], 3-p Student t [L], Truncated Exponential [L], Wakeby [L], and Weibull [L]. LMs have multivariate analogs; the sample L-comoments (LCMs) are implemented and might have considerable application with copulas because LCMs measure asymmetric association and higher comoments or comovements of variables.