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Existence and stability of a discrete probability distribution by maximum entropy approach. (English) Zbl 1017.62011
Summary: The discrete maximum entropy (ME) probability distribution which can take on a finite number of values and whose first moments are assigned, is considered. The necessary and sufficient conditions for the existence of a maximum entropy solution are identical to the general ones for the finite moment problem. The entropy decreasing by adding one more moment is studied. Unstability of the distribution recovering is proved when an increasing number of moments is used.

MSC:
62E10 Characterization and structure theory of statistical distributions
62B10 Statistical aspects of information-theoretic topics
60E05 Probability distributions: general theory
44A60 Moment problems
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