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Optimal predictive densities and fractional moments
Author(s) -
Taufer Emanuele,
Bose Sudip,
Tagliani Aldo
Publication year - 2008
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.721
Subject(s) - kullback–leibler divergence , mathematics , random variable , principle of maximum entropy , moment (physics) , entropy (arrow of time) , generalized method of moments , variable (mathematics) , sample size determination , distribution (mathematics) , sample (material) , mathematical optimization , statistics , statistical physics , mathematical analysis , physics , classical mechanics , quantum mechanics , estimator , thermodynamics
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.