Hosking, J. R. M. (1990).
L-moments: analysis and estimation of distributions
using linear combinations of order statistics.
Journal of the Royal Statistical Society, Series B,
52, 105-124.
Abstract.
L-moments are expectations of certain linear combinations of order
statistics.
They can be defined for any random variable whose mean exists
and form the basis of a general theory which covers the summarization
and description of theoretical probability distributions,
the summarization and description of observed data samples,
estimation of parameters and quantiles of probability distributions,
and hypothesis tests for probability distributions.
The theory involves such established procedures as the use
of order statistics and Gini's mean difference statistic, and gives
rise to some promising innovations such as the measures of skewness
and kurtosis described in section 2, and new methods of parameter
estimation for several distributions.
The theory of L-moments parallels the theory of (conventional)
moments, as the above list of applications might suggest.
The main advantage of L-moments over conventional moments is that
L-moments, being linear functions of the data, suffer less from the
effects of sampling variability: L-moments are more robust than
conventional moments to outliers in the data and enable more secure
inferences to be made from small samples about an underlying probability
distribution.
L-moments sometimes yield more efficient parameter estimates
than the maximum-likelihood estimates.
Author's note.
Supplementary results, mostly details of proofs, are available in
IBM Research Report RC14492.
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