Trimmed L-moments, defined by Elamir and Seheult (Comput. Statsist. Data Anal., 2003), summarize the shape of probability distributions or data samples in a way that remains viable for heavy-tailed distributions, even those for which the mean may not exist. We derive some further theoretical results concerning trimmed L-moments: a relation with the expansion of the quantile function as a weighted sum of Jacobi polynomials; the bounds that must be satisfied by trimmed L-moments; and recurrences between trimmed L-moments with different degrees of trimming. We also give examples how trimmed L-moments can be used, analogously to L-moments, in the analysis of heavy-tailed data. Examples include identification of distributions using a trimmed L-moment ratio diagram, shape parameter estimation for the generalized Pareto distribution, and fitting generalized Pareto distributions to a heavy-tailed data sample of computer network traffic.
By: J. R. M. Hosking
Published in: RC23783 in 2005
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