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.

翻译：受描述与信息度量相关的有用概念的需求驱动，本文引入了“概率密度函数相关分布”。这些分布是通过绝对连续随机变量在其自身概率密度函数下的变换来定义的。我们研究了这些分布的主要特征，包括分布的一般形式、分位数以及可靠性理论中的若干相关概念。这使我们能够进一步获得对指数型和拉普拉斯型分布而言，其概率密度函数相关分布为均匀分布的特征刻画。同时，本文借助适当的随机序解决了概率密度函数相关分布的随机比较问题。最后，利用所得结果分析并比较了某些有用的信息度量（如微分熵和方差熵）的性质。