Optimal predictive densities and fractional moments

Abstract

Abstract The maximum entropy approach used together with fractional moments has proven to be a flexible and powerful tool for density approximation of a positive random variable. In this paper we consider an optimality criterion based on the Kullback–Leibler distance in order to select appropriate fractional moments. We discuss the properties of the proposed procedure when all the available information comes from a sample of observations. The method is applied to the size distribution of the U.S. family income. Copyright © 2008 John Wiley & Sons, Ltd.