{"title":"Benford定律的简明证明","authors":"","doi":"10.1016/j.fmre.2023.01.002","DOIUrl":null,"url":null,"abstract":"<div><p>This article presents a concise proof of the famous Benford’s law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and elegant, accessible to anyone with basic knowledge of calculus, revealing that the law originates from the basic property of human number system. The criterion can bring great convenience to the field of fraud detection.</p></div>","PeriodicalId":34602,"journal":{"name":"Fundamental Research","volume":"4 4","pages":"Pages 841-844"},"PeriodicalIF":6.2000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2667325823000043/pdfft?md5=5e07d0c1d75831e9dc52d7a811dc3681&pid=1-s2.0-S2667325823000043-main.pdf","citationCount":"0","resultStr":"{\"title\":\"A concise proof of Benford’s law\",\"authors\":\"\",\"doi\":\"10.1016/j.fmre.2023.01.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This article presents a concise proof of the famous Benford’s law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and elegant, accessible to anyone with basic knowledge of calculus, revealing that the law originates from the basic property of human number system. The criterion can bring great convenience to the field of fraud detection.</p></div>\",\"PeriodicalId\":34602,\"journal\":{\"name\":\"Fundamental Research\",\"volume\":\"4 4\",\"pages\":\"Pages 841-844\"},\"PeriodicalIF\":6.2000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2667325823000043/pdfft?md5=5e07d0c1d75831e9dc52d7a811dc3681&pid=1-s2.0-S2667325823000043-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamental Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2667325823000043\",\"RegionNum\":3,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Multidisciplinary\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamental Research","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2667325823000043","RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Multidisciplinary","Score":null,"Total":0}
This article presents a concise proof of the famous Benford’s law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and elegant, accessible to anyone with basic knowledge of calculus, revealing that the law originates from the basic property of human number system. The criterion can bring great convenience to the field of fraud detection.
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