L-moments, Censored L-moments, Trimmed L-moments, L-comoments,
and Many Distributions
Description
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. The method of
L-moments can out perform the method of maximum likelihood. The
lmomco package historically is oriented around canonical
FORTRAN algorithms of J.R.M. Hosking, and the nomenclature for
many of the functions parallels that of the Hosking library,
which later became available in the lmom package. However, vast
arrays of various extensions and curiosities are added by the
author to aid and expand the breadth of L-moment application.
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 and also by indicator variable also
are available. E.A.H. Elamir and A.H. Seheult have developed
the trimmed L-moments, which are implemented in this package,
and numerical integration of quantile functions is used to
dynamically compute trajectories of select TL-moment ratios for
the construction of TL-moment ratio diagrams. Robert Serfling
and Peng Xiao have extended L-moments into multivariate space;
the so-called sample L-comoments are implemented here and might
have considerable application in copula theory because they
measure asymmetric correlation and higher co-moments or
co-movements of variables. 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), 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), 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).