Eliazar Iddo
School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel.
Entropy (Basel). 2024 Jun 30;26(7):565. doi: 10.3390/e26070565.
This paper establishes a general framework for measuring statistical divergence. Namely, with regard to a pair of random variables that share a common range of values: quantifying the distance of the statistical distribution of one random variable from that of the other. The general framework is then applied to the topics of socioeconomic inequality and renewal processes. The general framework and its applications are shown to yield and to relate to the following: f-divergence, Hellinger divergence, Renyi divergence, and Kullback-Leibler divergence (also known as relative entropy); the Lorenz curve and socioeconomic inequality indices; the Gini index and its generalizations; the divergence of renewal processes from the Poisson process; and the divergence of anomalous relaxation from regular relaxation. Presenting a 'fresh' perspective on statistical divergence, this paper offers its readers a simple and transparent construction of statistical-divergence gauges, as well as novel paths that lead from statistical divergence to the aforementioned topics.
本文建立了一个用于度量统计散度的通用框架。具体而言，针对一对具有共同取值范围的随机变量：量化一个随机变量的统计分布与另一个随机变量的统计分布之间的距离。然后将该通用框架应用于社会经济不平等和更新过程等主题。结果表明，该通用框架及其应用产生并涉及以下内容：f散度、赫林格散度、雷尼散度和库尔贝克-莱布勒散度（也称为相对熵）；洛伦兹曲线和社会经济不平等指数；基尼指数及其推广；更新过程与泊松过程的散度；以及反常弛豫与常规弛豫的散度。本文从“全新”视角看待统计散度，为读者提供了统计散度度量的简单透明构建方法，以及从统计散度通向上述主题的新路径。
