L-moments, Trimmed L-moments, L-comoments, and Many Distributions
Description
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.
Numerous additional features are added to aid in extension of the breadth 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) include the Cauchy(TL), Exponential(L), Gamma(L), Generalized Extreme
Value(L), Generalized Lambda(L/TL), Generalized Logistic (L), Generalized
Normal(L), Generalized Pareto(L/TL), Gumbel(L), Normal(L), Kappa(L), Pearson
Type III(L), Wakeby(L), and Weibull(L).