Maximum Entropy in the Finite Hausdorff Moment Problem
نویسنده
چکیده
The maximum entropy (M.E.) approach to the nite Hausdorr moment problem is studied, a new approach to prove the necessary and suucient conditions for the existence of M.E. solution is considered by transforming the moment problem into a system of ordinary diierential equations. The new technique allows also to prove entropy convergence of the resulting sequence of maximum entropy extimators, and is generalized, in another work, to solve also the Stieltjes and Hamburger nite moment problem.
منابع مشابه
Maximum entropy solutions and moment problem in unbounded domains
The classical Stieltjes and Hamburger moment problems in the maximum entropy approach have been reconsidered. Incorrect conditions of existence, previously appeared in literature, have been reviewed and improved. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords-Entropy, Hankel matrix, Hausdorff, Hamburger, Stieltjee moment problems, Moment space.
متن کاملModeling of the Maximum Entropy Problem as an Optimal Control Problem and its Application to Pdf Estimation of Electricity Price
In this paper, the continuous optimal control theory is used to model and solve the maximum entropy problem for a continuous random variable. The maximum entropy principle provides a method to obtain least-biased probability density function (Pdf) estimation. In this paper, to find a closed form solution for the maximum entropy problem with any number of moment constraints, the entropy is consi...
متن کاملHausdorff moment problem and maximum entropy: A unified approach
Hausdor moment problem in the approach of maximum entropy is reconsidered. Some aspects, as existence condition, entropy convergence, entropy decreasing, stability are studied through a uni®ed approach. Results known in literature and some new ones are illustrated Ó 1999 Elsevier Science Inc. All rights reserved. Keywords: Convex hull; Entropy; Hankel determinant; Moment problem 1. Introductio...
متن کاملPii: S0893-9659(01)00136-7
K e y w o r d s C o n v e x hull, Entropy, Hankel matrix, Moment problem. 1. I N T R O D U C T I O N Every probability distribution has some uncertainty associated with it, and its entropy provides a quantitat ive measure of this uncertainty. Partial information given, for instance, in terms of averages about a random variate decreases its entropy. It thus appears interesting to provide an entr...
متن کاملMaximum Entropy in the Finite Stielties and Hamburger Moment Problem
A necessary and suucient condition for the existence of the maximum entropy (ME) function deened in an innnite or semiinnnite interval, is provided. The conclusions reached show that, except in a few particular cases, the necessary and suucient conditions for the existence of maximum entropy function are identical to the conditions for the solution of the moment problem when the rst M+1 moments...
متن کامل