高斯与恒等函数--正态分布的刻画
Gauss and the identity function -- a tale of characterizations of the normal distribution
摘要：
正态分布是众所周知的几个结果，它是唯一满足。本文的目的是表明，许多这些特征实际上遵循的事实，即正态分布的对数密度的导数是（负）的身份功能。这\emph{a priori}非常简单但令人惊讶的观察允许更深入地了解现有的表征，并铺平了道路，立即扩展到一个一般密度$x\mapsto p(x)$，取代$-x$在这些结果与$(\log p(x))'$。
英文摘要：
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 $(\log p(x))'$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
