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Stimulated by the need of describing useful notions related to informationmeasures, we introduce the `pdf-related distributions'. These are defined interms of transformation of absolutely continuous random variables through theirown probability density functions. We investigate their main characteristics,with reference to the general form of the distribution, the quantiles, and somerelated notions of reliability theory. This allows us to obtain acharacterization of the pdf-related distribution being uniform fordistributions of exponential and Laplace type as well. We also face the problemof stochastic comparing the pdf-related distributions by resorting to suitablestochastic orders. Finally, the given results are used to analyse propertiesand to compare some useful information measures, such as the differentialentropy and the varentropy.

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