Reconstructing heavy-tailed distributions by splicing with maximum entropy in the mean

Santiago Carrillo, Henryk Gzyl and Aldo Tagliani

Abstract

ABSTRACT

Sometimes it is not possible to obtain a single parametric density with the desired tail behavior to fit a given data set. Splicing two different parametric densities is a useful process in such cases. Since the two parts depend on local data, a question arises over how best to assemble the two parts so that the properties of the whole data set are taken into account. We propose an application of the method of maximum entropy in the mean to splice the two parts together in such a way that the resulting global density has the first two moments of the full data set.