Uncertainty, entropy and moments problem

Abstract

The recovering of a positive density function of which a finite number of moments are assigned is considered from the point of view of maximum entropy approach. The questions concerning the existence, convergence and numerical aspects underlying the practical use of maximum entropy distributions in Statistics are considered. The Hausdorff, Stieltjes and Hamburger momento problem are separately analyzed. The advantages stemming from the use of maximum entropy approach, compared to other approaches, are illustrated.