当分数函数是恒等函数时——正态分布特征的一个故事

IF 2 Q2 ECONOMICS

Econometrics and Statistics Pub Date : 2023-04-01 DOI:10.1016/j.ecosta.2020.10.001

Christophe Ley

{"title":"当分数函数是恒等函数时——正态分布特征的一个故事","authors":"Christophe Ley","doi":"10.1016/j.ecosta.2020.10.001","DOIUrl":null,"url":null,"abstract":"<div><p><span>The normal distribution is well-known for several results that it is the only to fulfil. Much less well-known is the fact that many of these characterizations follow from the fact that the derivative of the log-density of the normal distribution is the (negative) identity function. This </span><em>a priori</em> very simple yet surprising observation allows a deeper understanding of existing characterizations and paves the way for an immediate extension of various seemingly normal-based characterizations to a general density by replacing the (negative) identity function in these results with the derivative of that log-density.</p></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"26 ","pages":"Pages 153-160"},"PeriodicalIF":2.0000,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.ecosta.2020.10.001","citationCount":"2","resultStr":"{\"title\":\"When the score function is the identity function - A tale of characterizations of the normal distribution\",\"authors\":\"Christophe Ley\",\"doi\":\"10.1016/j.ecosta.2020.10.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>The normal distribution is well-known for several results that it is the only to fulfil. Much less well-known is the fact that many of these characterizations follow from the fact that the derivative of the log-density of the normal distribution is the (negative) identity function. This </span><em>a priori</em> very simple yet surprising observation allows a deeper understanding of existing characterizations and paves the way for an immediate extension of various seemingly normal-based characterizations to a general density by replacing the (negative) identity function in these results with the derivative of that log-density.</p></div>\",\"PeriodicalId\":54125,\"journal\":{\"name\":\"Econometrics and Statistics\",\"volume\":\"26 \",\"pages\":\"Pages 153-160\"},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2023-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.ecosta.2020.10.001\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Econometrics and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2452306220300836\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Econometrics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2452306220300836","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}

引用次数: 2

摘要

正态分布是众所周知的几个结果，它是唯一可以实现的。不太为人所知的是，这些特征中的许多都源于正态分布的对数密度的导数是（负）单位函数这一事实。这种先验的、非常简单但令人惊讶的观察结果允许对现有特征进行更深入的理解，并通过用对数密度的导数替换这些结果中的（负）同一函数，为各种看似正常的特征立即扩展到一般密度铺平了道路。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

When the score function is the identity function - A tale of characterizations of the normal distribution

The normal distribution is well-known for several results that it is the only to fulfil. Much less well-known is the fact that many of these characterizations follow from the fact that the derivative of the log-density of the normal distribution is the (negative) identity function. This a priori very simple yet surprising observation allows a deeper understanding of existing characterizations and paves the way for an immediate extension of various seemingly normal-based characterizations to a general density by replacing the (negative) identity function in these results with the derivative of that log-density.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Econometrics and Statistics ECONOMICS-

CiteScore

3.10

自引率

10.50%

发文量

期刊介绍： Econometrics and Statistics is the official journal of the networks Computational and Financial Econometrics and Computational and Methodological Statistics. It publishes research papers in all aspects of econometrics and statistics and comprises of the two sections Part A: Econometrics and Part B: Statistics.