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
Hauptverfasser: Crescenzo, Antonio Di, Paolillo, Luca, Suárez-Llorens, Alfonso
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Heidelberg Springer Nature B.V 01.01.2025
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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.
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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  surname: Paolillo
  fullname: Paolillo, Luca
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  givenname: Alfonso
  orcidid: 0000-0002-7679-9328
  surname: Suárez-Llorens
  fullname: Suárez-Llorens, Alfonso
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Cites_doi 10.1051/ps/2020028
10.1007/BF00054789
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SubjectTerms Entropy
Entropy (Information theory)
Information theory
Lifetime
Probability density functions
Random variables
Title Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions
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