Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions

Antonio Di Crescenzo (), Luca Paolillo () and Alfonso Suárez-Llorens ()
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Antonio Di Crescenzo: Università degli Studi di Salerno
Luca Paolillo: Università degli Studi di Salerno
Alfonso Suárez-Llorens: Universidad de Cádiz

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 1, No 3, 43-59

Abstract: 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.

Keywords: Differential entropy; Differential varentropy; Stochastic orders; Information measures; Decreasing rearrangement; 60E05; 60E15; 62E99; 94A17 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-024-00947-3

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