L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments,
and Many Distributions
Description
Extensive functions for L-moments (LMs) and probability-weighted moments
(PWMs), parameter estimation for distributions, LM computation for distributions, and
L-moment ratio diagrams. Maximum likelihood and maximum product of spacings estimation
are also available. LMs for right-tail and left-tail censoring by known or unknown threshold
and by indicator variable are available. Asymmetric (asy) trimmed LMs (TL-moments, TLMs) are
supported. LMs of residual (resid) and reversed (rev) residual life are implemented along
with 13 quantile function operators for reliability and survival analyses. Exact analytical
bootstrap estimates of order statistics, LMs, and variances-covariances of LMs are provided.
The Harri-Coble Tau34-squared Normality Test is available. Distribution support with
"L" (LMs), "TL" (TLMs) and added (+) support for right-tail censoring (RC) encompasses:
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], Polynomial Density-
Quantile 3 and 4[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]. Multivariate
sample L-comoments (LCMs) are implemented to measure asymmetric associations.