Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions
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 charact...
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| Veröffentlicht in: | Metrika Jg. 88; H. 1; S. 43 - 59 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Suárez-Llorens, Alfonso Crescenzo, Antonio Di Paolillo, Luca |
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| Cites_doi | 10.1051/ps/2020028 10.1007/BF00054789 10.2307/3213709 10.1007/978-0-387-34675-5 10.1016/S0167-7152(96)00152-6 10.1007/s00184-018-0667-y 10.21136/AM.2017.0182-16 10.1007/978-3-319-40519-3_3 10.2307/3214465 10.1017/S0269964820000133 10.1017/S0269964815000376 10.1214/14-STS430 10.1016/0167-7152(88)90047-8 10.1016/0167-7152(83)90054-8 10.1016/S0020-0255(03)00156-7 10.1017/S0269964803171069 10.1214/aoms/1177728261 10.1016/0167-7152(95)00141-7 10.1016/j.cam.2017.01.001 |
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| Title | Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions |
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