  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 uniform distribution based on pdf-related 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.
