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.

翻译：由于需要说明与信息计量有关的有用概念,我们引入了“与pdf有关的分布”,这些分布的定义是通过其自身概率密度函数对绝对连续随机变量进行转换。我们根据分布的一般形式、四分位数和一些相关的可靠性理论概念,调查其主要特征。这使我们能够根据与pdf有关的指数和拉比特类型分布,对统一分布进行定性。我们还面临着通过采用适当的随机命令对与pdf有关的分布进行比较的随机问题。最后,所给的结果被用来分析属性和比较一些有用的信息措施,如差异的酶和变形。