Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866914777967624192 |
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| author | Di Crescenzo, Antonio Paolillo, Luca Suarez-Llorens, Alfonso |
| author_facet | Di Crescenzo, Antonio Paolillo, Luca Suarez-Llorens, Alfonso |
| contents | Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own probability density functions. We investigate their main characteristics, with reference to the general form of the distribution, the quantiles, and some related notions of reliability theory. This allows us to obtain a characterization of the pdf-related distribution being uniform for distributions of exponential and Laplace type as well. We also face the problem of stochastic comparing the pdf-related distributions by resorting to suitable stochastic orders. Finally, the given results are used to analyse properties and to compare some useful information measures, such as the differential entropy and the varentropy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2103_11038 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions Di Crescenzo, Antonio Paolillo, Luca Suarez-Llorens, Alfonso Probability Information Theory Statistics Theory 60E05, 60E15, 62E99, 94A17 Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own probability density functions. We investigate their main characteristics, with reference to the general form of the distribution, the quantiles, and some related notions of reliability theory. This allows us to obtain a characterization of the pdf-related distribution being uniform for distributions of exponential and Laplace type as well. We also face the problem of stochastic comparing the pdf-related distributions by resorting to suitable stochastic orders. Finally, the given results are used to analyse properties and to compare some useful information measures, such as the differential entropy and the varentropy. |
| title | Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions |
| topic | Probability Information Theory Statistics Theory 60E05, 60E15, 62E99, 94A17 |
| url | https://arxiv.org/abs/2103.11038 |