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Probability distributions and the maximum entropy principle

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  • Villa-Morales, José
  • Rincón, Luis

Abstract

It is shown that every probability distribution with finite entropy can be characterized as the minimum relative entropy distribution respect to a given non-negative function within a non-trivial collection of probability distributions. This result is extended to families of distributions. We also study sufficient conditions to guarantee the existence and uniqueness of a distribution with maximum entropy on certain families of distributions. Also several examples are presented of how the general results can be applied.

Suggested Citation

  • Villa-Morales, José & Rincón, Luis, 2023. "Probability distributions and the maximum entropy principle," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    • Handle: RePEc:eee:apmaco:v:444:y:2023:i:c:s0096300322008748
    DOI: 10.1016/j.amc.2022.127806
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    References listed on IDEAS

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    1. Peter Hall & Sally Morton, 1993. "On the estimation of entropy," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(1), pages 69-88, March.
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