{"id":230,"date":"2023-08-03T21:57:52","date_gmt":"2023-08-03T21:57:52","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%9c%ac%e7%a6%8f%e5%be%b7%e5%ae%9a%e5%be%8b\/"},"modified":"2023-08-03T21:57:52","modified_gmt":"2023-08-03T21:57:52","slug":"%e6%9c%ac%e7%a6%8f%e5%be%b7%e5%ae%9a%e5%be%8b","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%9c%ac%e7%a6%8f%e5%be%b7%e5%ae%9a%e5%be%8b\/","title":{"rendered":"\u672c\u798f\u5fb7\u5b9a\u5f8b"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u672c\u798f\u5fb7\u5b9a\u5f8b\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u4e86\u89e3\u672c\u798f\u5fb7\u5b9a\u5f8b\u662f\u5982\u4f55\u88ab\u53d1\u73b0\u7684\u4ee5\u53ca\u8be5\u7edf\u8ba1\u5b9a\u5f8b\u7684\u5e94\u7528\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-ley-de-benford\"><\/span>\u4ec0\u4e48\u662f\u672c\u798f\u5fb7\u5b9a\u5f8b\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u672c\u798f\u5fb7\u5b9a\u5f8b<\/strong>\uff0c\u4e5f\u79f0\u4e3a<strong>\u7b2c\u4e00\u4f4d\u6570\u5b57\u5b9a\u5f8b<\/strong>\uff0c\u662f\u4e00\u79cd\u7edf\u8ba1\u5b9a\u5f8b\uff0c\u8868\u793a\u4e00\u6bb5\u6570\u636e\u7684\u7b2c\u4e00\u4f4d\u6570\u5b57\u4e3a 1 \u7684\u6982\u7387\u5927\u4e8e\u5b83\u4e3a\u53e6\u4e00\u4e2a\u6570\u5b57\u7684\u6982\u7387\u3002<\/p>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u672c\u798f\u5fb7\u5b9a\u5f8b\u8bf4\u7684\u662f\uff0c\u5728\u73b0\u5b9e\u751f\u6d3b\u4e2d\u5b58\u5728\u7684\u4e00\u7ec4\u6570\u503c\u6570\u636e\u4e2d\uff0c\u6570\u5b571\u662f\u4f5c\u4e3a\u6570\u636e\u7b2c\u4e00\u4f4d\u91cd\u590d\u6b21\u6570\u6700\u591a\u7684\u6570\u5b57\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u6570\u5b57\u8d8a\u9ad8\uff0c\u6700\u7ec8\u83b7\u5f97\u7b2c\u4e00\u540d\u7684\u53ef\u80fd\u6027\u5c31\u8d8a\u5c0f\u3002\u56e0\u6b64\uff0c\u7b2c\u4e00\u4e2a\u6570\u5b57\u66f4\u6709\u53ef\u80fd\u662f 1\uff0c\u800c\u4e0d\u662f 2\uff0c\u4f46 2 \u6bd4 3 \u66f4\u6709\u53ef\u80fd\uff0c3 \u6bd4 4 \u66f4\u6709\u53ef\u80fd\uff0c\u4f9d\u6b64\u7c7b\u63a8\u3002<\/p>\n<p>\u672c\u798f\u5fb7\u5b9a\u5f8b\u5f97\u540d\u4e8e\u7f8e\u56fd\u4eba\u5f17\u5170\u514b\u00b7\u672c\u798f\u5fb7\u3002\u5c3d\u7ba1\u672c\u798f\u5fb7\u4e0d\u662f\u4ed6\u53d1\u660e\u7684\uff0c\u4f46\u4ed6\u666e\u53ca\u4e86\u8fd9\u4e00\u7edf\u8ba1\u89c4\u5219\u3002\u4e0b\u9762\u6211\u4eec\u5c31\u6765\u770b\u770b\u672c\u798f\u5fb7\u5b9a\u5f8b\u7684\u7531\u6765\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-ley-de-benford\"><\/span>\u672c\u798f\u5fb7\u5b9a\u5f8b\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u672c\u798f\u5fb7\u5b9a\u5f8b\u6307\u51fa\uff0c\u7b2c\u4e00\u4e2a\u6570\u5b57\u662f\u67d0\u4e2a\u6570\u5b57\u7684\u6982\u7387\u7b49\u4e8e\u8be5\u6570\u5b57\u7684\u4e00\u52a0\u4e00\u7684\u5bf9\u6570\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u672c\u798f\u5fb7\u5b9a\u5f8b\u7684\u516c\u5f0f<\/strong>\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a77defb5b209293a074ac2bee02c2e07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle P[X=d]=\\log_{10}\\left(1+\\frac{1}{d}\\right)\\\\[4ex]d=1,2,3,\\ldots ,9\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"203\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4ece\u672c\u798f\u5fb7\u5b9a\u5f8b\u516c\u5f0f\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u6bcf\u4e2a\u6570\u5b57\u662f\u6570\u636e\u9879\u7b2c\u4e00\u4f4d\u6570\u5b57\u7684\u6982\u7387\u3002\u5728\u4e0b\u8868\u4e2d\u60a8\u53ef\u4ee5\u770b\u5230\u6240\u6709\u6982\u7387\u7684\u767e\u5206\u6bd4\uff1a <\/p>\n<figure class=\"wp-block-table aligncenter is-style-stripes\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">\u6570\u5b57<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">\u6982\u7387<br \/>\u662f\u7b2c\u4e00\u4e2a\u6570\u5b57<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">1<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 30.1%<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 2<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 17.6%<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 12.5%<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 4<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 9.7%<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 5<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 7.9%<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 6<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 6.7%<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 7<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 5.8%<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 8<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 5.1%<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 9<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 4.6%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u6b64\u5916\uff0c\u60a8\u53ef\u4ee5\u5728\u4e0b\u9762\u770b\u5230\u4e00\u4e2a\u76f4\u65b9\u56fe\uff0c\u5176\u4e2d\u4ee5\u56fe\u5f62\u65b9\u5f0f\u8868\u793a\u4e86\u672c\u798f\u5fb7\u5b9a\u5f8b\u7684\u6240\u6709\u6982\u7387\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/loi-de-benford.png\" alt=\"\u672c\u798f\u5fb7\u5b9a\u5f8b\" class=\"wp-image-4585\" width=\"459\" height=\"310\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"historia-de-la-ley-de-benford\"><\/span>\u672c\u798f\u5fb7\u5b9a\u5f8b\u7684\u5386\u53f2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1881 \u5e74\uff0c\u6570\u5b66\u5bb6\u897f\u8499\u00b7\u7ebd\u79d1\u59c6 (Simon Newcomb) \u53d1\u73b0\u5bf9\u6570\u8868\u7684\u7b2c\u4e00\u9875\u6bd4\u6700\u540e\u4e00\u9875\u7684\u4f7f\u7528\u6b21\u6570\u8981\u591a\u5f97\u591a\uff0c\u7531\u6b64\u63a8\u5bfc\u51fa\u4e86\u672c\u798f\u5fb7\u5b9a\u5f8b\u3002\u8fd9\u610f\u5473\u7740\u6570\u5b57\u7684\u524d\u51e0\u4e2a\u6570\u5b57\u51fa\u73b0\u7684\u53ef\u80fd\u6027\u5e76\u4e0d\u76f8\u540c\uff0c\u4f46 1 \u6bd4 2 \u51fa\u73b0\u7684\u9891\u7387\u66f4\u9ad8\uff0c2 \u6bd4 3 \u51fa\u73b0\u7684\u9891\u7387\u66f4\u9ad8\uff0c\u4f9d\u6b64\u7c7b\u63a8\uff0c\u76f4\u5230 9\u3002<\/p>\n<p>\u7136\u800c\uff0c\u7ebd\u79d1\u59c6\u6ca1\u6709\u7559\u4e0b\u4efb\u4f55\u7edf\u8ba1\u8bc1\u636e\u6765\u8868\u660e\u8fd9\u6761\u89c4\u5219\u88ab\u9075\u5faa\uff0c\u4ed6\u53ea\u662f\u6839\u636e\u5bf9\u6570\u8868\u7684\u78e8\u635f\u8fdb\u884c\u4e86\u63a8\u6f14\u3002<\/p>\n<p>\u540e\u6765\uff0c\u7279\u522b\u662f\u5728 1938 \u5e74\uff0c\u7269\u7406\u5b66\u5bb6\u5f17\u5170\u514b\u00b7\u672c\u798f\u5fb7\uff08Frank Benford\uff09\u4e5f\u505a\u51fa\u4e86\u540c\u6837\u7684\u89c2\u5bdf\uff0c\u5e76\u505a\u4e86\u4e00\u4e2a\u5b9e\u9a8c\u6765\u5b9e\u8bc1\u9a8c\u8bc1\u3002\u5728\u6765\u81ea20\u4e2a\u4e0d\u540c\u6837\u672c\u768420,229\u4e2a\u503c\u7684\u7edf\u8ba1\u6570\u636e\u96c6\u4e0a\uff0c\u4ed6\u5bf9\u6bcf\u4e2a\u6570\u636e\u7684\u7b2c\u4e00\u4f4d\u6570\u5b57\u8fdb\u884c\u4e86\u7814\u7a76\u3002\u56e0\u6b64\uff0c\u6839\u636e\u7ed3\u679c\uff0c\u4ed6\u8bc1\u660e\u4e86\u672c\u798f\u5fb7\u5b9a\u5f8b\u7684\u6ee1\u8db3\uff0c\u5e76\u63a8\u5bfc\u51fa\u4e86\u4e00\u4e2a\u516c\u5f0f\uff0c\u4f7f\u4ed6\u80fd\u591f\u8ba1\u7b97\u51fa\u7b2c\u4e00\u4e2a\u6570\u5b57\u662f\u67d0\u4e2a\u6570\u5b57\u7684\u6982\u7387\uff08\u6211\u4eec\u5728\u4e0a\u9762\u770b\u5230\u4e86\u8fd9\u4e2a\u516c\u5f0f\uff09\u3002<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u867d\u7136\u672c\u798f\u5fb7\u5b9a\u5f8b\u662f\u7531\u897f\u8499\u00b7\u7ebd\u79d1\u59c6\uff08Simon Newcomb\uff09\u9996\u5148\u53d1\u73b0\u7684\uff0c\u4f46\u4ed6\u4ee5\u5f17\u5170\u514b\u00b7\u672c\u798f\u5fb7\uff08Frank Benford\uff09\u7684\u540d\u5b57\u547d\u540d\uff0c\u56e0\u4e3a\u4ed6\u662f\u9a8c\u8bc1\u8fd9\u4e00\u7edf\u8ba1\u5b9a\u5f8b\u7684\u4eba\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-ley-de-benford\"><\/span>\u672c\u798f\u5fb7\u5b9a\u5f8b\u7684\u5e94\u7528<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u672c\u798f\u5fb7\u5b9a\u5f8b\u662f\u4e00\u79cd\u7edf\u8ba1\u5b9a\u5f8b\uff0c\u53ef\u5e94\u7528\u4e8e\u975e\u5e38\u4e0d\u540c\u7684\u9886\u57df\u3002\u4f8b\u5982\uff0c\u672c\u798f\u5fb7\u5b9a\u5f8b\u5e7f\u6cdb\u5e94\u7528\u4e8e\u7ecf\u6d4e\u5b66\u3001\u751f\u7269\u5b66\uff0c\u751a\u81f3\u653f\u6cbb\u5b66\u3002<\/p>\n<p>\u5728\u7ecf\u6d4e\u5b66\u4e2d\uff0c\u672c\u798f\u5fb7\u5b9a\u5f8b\u7ecf\u5e38\u88ab\u7528\u6765\u68c0\u6d4b\u6570\u636e\u64cd\u7eb5\uff0c\u56e0\u4e3a\u5982\u679c\u4e00\u4e2a\u6570\u636e\u96c6\u4e0d\u7b26\u5408\u672c\u798f\u5fb7\u5b9a\u5f8b\uff0c\u5c31\u8868\u660e\u8be5\u6570\u636e\u88ab\u64cd\u7eb5\u4e86\u3002\u4f8b\u5982\uff0c\u8be5\u6cd5\u5f8b\u7528\u4e8e\u4fa6\u67e5\u53ef\u80fd\u7684\u7a0e\u52a1\u6b3a\u8bc8\u6848\u4ef6\u3002<\/p>\n<p>\u5e94\u8be5\u6ce8\u610f\u7684\u662f\uff0c\u672c\u798f\u5fb7\u5b9a\u5f8b\u4e0d\u7528\u4e8e\u8bc1\u660e\u968f\u673a\u73b0\u8c61\u7684\u771f\u5b9e\u6027\uff0c\u56e0\u4e3a\u7ed3\u679c\u662f\u7b49\u6982\u7387\u7684\u3002\u56e0\u6b64\uff0c\u672c\u798f\u5fb7\u89c4\u5219\u4e0d\u80fd\u7528\u4e8e\u9a8c\u8bc1\u5f69\u7968\u7ed3\u679c\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5728\u9057\u4f20\u5b66\u4e2d\uff0c\u672c\u798f\u5fb7\u5b9a\u5f8b\u53ef\u7528\u4e8e\u5206\u6790\u4e0d\u540c\u7c7b\u578b\u751f\u7269\u4e4b\u95f4\u57fa\u56e0\u7ec4\u957f\u5ea6\u7684\u5dee\u5f02\u3002<\/p>\n<p>\u6700\u540e\uff0c\u8fd8\u5c1d\u8bd5\u901a\u8fc7\u5e94\u7528\u672c\u798f\u5fb7\u5b9a\u5f8b\u6765\u68c0\u6d4b\u9009\u6c11\u6b3a\u8bc8\uff0c\u5c3d\u7ba1\u5b83\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u7684\u6709\u7528\u6027\u53d7\u5230\u8d28\u7591\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u672c\u798f\u5fb7\u5b9a\u5f8b\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u4e86\u89e3\u672c\u798f\u5fb7\u5b9a\u5f8b\u662f\u5982\u4f55\u88ab\u53d1\u73b0\u7684\u4ee5\u53ca\u8be5\u7edf\u8ba1\u5b9a\u5f8b\u7684\u5e94\u7528\u3002 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