截断分布族的方差与熵

Variance and Entropy of Truncated Family of Distributions

摘要: 熵和方差都是用来量化信息或数据的特性的重要工具，截断型分布是一类常见分布。本文研究了截断型分布族中熵和方差之间的关系：首先研究了一般形式的截断性分布中熵和方差，并分析了它们之间的关系；之后研究了三种特殊截断型分布：截断均匀分布、截断正态分布和截断Pareto分布，分别计算它们的熵和方差，并深入探讨了它们之间的关联性与相互影响。

Abstract: Entropy and variance are essential metrics employed to quantify the properties of information or data, with truncated distribution being a prevalent type of distribution. This paper delves into the interrelation between entropy and variance within the truncated distribution family. Initially, the investigation pertains to entropy and variance in the context of general truncated distribution, analyzing their relationship. Then we study three special truncation distributions: truncated uniform distribution, truncated normal distribution and truncated Pareto distribution, calculate their entropy and variance respectively, and deeply discuss their correlation and mutual influence.