Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter
We consider two types of entropy, namely, Shannon and Rényi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More precisely, we prove that both entropies increase with intensity. While for Shannon entropy the proof is comparatively simpl...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2024-07-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://journals.vu.lt./nonlinear-analysis/article/view/35845 |
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| author | Volodymyr Braiman Anatoliy Malyarenko Yuliya Mishura Yevheniia Anastasiia Rudyk |
| author_facet | Volodymyr Braiman Anatoliy Malyarenko Yuliya Mishura Yevheniia Anastasiia Rudyk |
| author_sort | Volodymyr Braiman |
| collection | DOAJ |
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We consider two types of entropy, namely, Shannon and Rényi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More precisely, we prove that both entropies increase with intensity. While for Shannon entropy the proof is comparatively simple, for Rényi entropy, which depends on additional parameter α > 0, we can characterize it as nontrivial. The proof is based on application of Karamata’s inequality to the terms of Poisson distribution.
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| format | Article |
| id | doaj-art-498c28a7ebda4b2d89e308bf85492831 |
| institution | DOAJ |
| issn | 1392-5113 2335-8963 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj-art-498c28a7ebda4b2d89e308bf854928312025-08-20T03:16:28ZengVilnius University PressNonlinear Analysis1392-51132335-89632024-07-0129410.15388/namc.2024.29.35560Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameterVolodymyr Braiman0Anatoliy Malyarenko1Yuliya Mishura2Yevheniia Anastasiia RudykTaras Shevchenko National University of KyivMälardalen UniversityTaras Shevchenko National University of Kyiv We consider two types of entropy, namely, Shannon and Rényi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More precisely, we prove that both entropies increase with intensity. While for Shannon entropy the proof is comparatively simple, for Rényi entropy, which depends on additional parameter α > 0, we can characterize it as nontrivial. The proof is based on application of Karamata’s inequality to the terms of Poisson distribution. https://journals.vu.lt./nonlinear-analysis/article/view/35845Shannon entropyRényi entropyPoisson distributionKaramata’s inequality |
| spellingShingle | Volodymyr Braiman Anatoliy Malyarenko Yuliya Mishura Yevheniia Anastasiia Rudyk Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter Nonlinear Analysis Shannon entropy Rényi entropy Poisson distribution Karamata’s inequality |
| title | Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter |
| title_full | Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter |
| title_fullStr | Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter |
| title_full_unstemmed | Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter |
| title_short | Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter |
| title_sort | properties of shannon and renyi entropies of the poisson distribution as the functions of intensity parameter |
| topic | Shannon entropy Rényi entropy Poisson distribution Karamata’s inequality |
| url | https://journals.vu.lt./nonlinear-analysis/article/view/35845 |
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