论文标题
高斯和身份函数 - 正态分布的特征的故事
Gauss and the identity function -- a tale of characterizations of the normal distribution
论文作者
论文摘要
正态分布是众所周知的，因为它是唯一要实现的结果。本文的目的是表明，许多这些特征实际上源于以下事实：正态分布的对数密度的导数是（负）身份函数。此\ emph {a先验}非常简单但令人惊讶的观察结果可以更深入地了解现有的特征，并通过用$（\ log p（x））'$替换这些结果中的$ -X $来立即扩展到一般密度$ x \ mapsto p（x）$。
The normal distribution is well-known for several results that it is the only to fulfil. The aim of the present paper is to show that many of these characterizations actually follow from the fact that the derivative of the log-density of the normal distribution is the (negative) identity function. This \emph{a priori} very simple yet surprising observation allows a deeper understanding of existing characterizations and paves the way to an immediate extension to a general density $x\mapsto p(x)$ by replacing $-x$ in these results with $(\log p(x))'$.
