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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Bibliographic Details
Published in:Metrika Vol. 88; no. 1; pp. 43 - 59
Main Authors: Crescenzo, Antonio Di, Paolillo, Luca, Suárez-Llorens, Alfonso
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01.01.2025
Subjects:
Entropy
Entropy (Information theory)
Information theory
Lifetime
Probability density functions
Random variables
ISSN:0026-1335, 1435-926X
Online Access:Get full text
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Summary: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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ISSN:0026-1335
1435-926X
DOI:10.1007/s00184-024-00947-3