Resumen
We find the distribution that has maximum entropy conditional on having specified values of its first rL-moments. This condition is equivalent to specifying the expected values of the order statistics of a sample of size r. The maximum-entropy distribution has a density-quantile function, the reciprocal of the derivative of the quantile function, that is a polynomial of degree r; the quantile function of the distribution can then be found by integration. This class of maximum-entropy distributions includes the uniform, exponential and logistic, and two new generalizations of the logistic distribution. It provides a new method of nonparametric fitting of a distribution to a data sample. We also derive maximum-entropy distributions subject to constraints on expected values of linear combinations of order statistics.

Resumen
Trimmed L-moments, defined by Elamir and Seheult [2003. Trimmed L-moments. Comput. Statist. Data Anal. 43, 299–314], 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; recurrences between trimmed L-moments with different degrees of trimming; and the asymptotic distributions of sample estimators of trimmed L-moments. We also give examples of 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.