Title: On the existence of maximum entropy distributions with four and more assigned moments
Abstract: It is known that the probability distribution e− ∑04ajXj satisfy the Maximum Entropy Principle (MEP) if the available data consist in four moments of probability density function. Two problems are typically associated with use of MEP: the definition of the range of acceptable values for the moments Mi; the evaluation of the coefficients aj. Both problems have already been accurately resolved by analytical procedures when the first two moments of the distribution are known. In this work, the analytical solution in the case of four known moments is provided and a criterion for confronting the general case (whatever the number of known moments) is expounded. The first four moments are expressed in nondimensional form through the expectation and the coefficients of variation, skewness and kurtosis. The range of their acceptable values is obtained from the analytical properties of the differential equations which govern the problem and from the Schwarz inequality.
Publication Year: 1990
Publication Date: 1990-12-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 15
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