{"id":12729,"date":"2018-11-11T01:00:00","date_gmt":"2018-11-10T17:00:00","guid":{"rendered":"http:\/\/swarma.org\/%e5%85%b3%e4%ba%8e%e5%b9%82%e5%be%8b%e5%88%86%e5%b8%83%ef%bc%8c%e4%bd%a0%e8%bf%98%e5%ba%94%e8%af%a5%e7%9f%a5%e9%81%93%e5%a6%82%e4%bd%95%e7%94%a8%e4%bb%a3%e7%a0%81%e5%ae%9e%e7%8e%b0%ef%bc%81-%e9%9b%86\/"},"modified":"2019-01-02T18:31:10","modified_gmt":"2019-01-02T10:31:10","slug":"%e5%85%b3%e4%ba%8e%e5%b9%82%e5%be%8b%e5%88%86%e5%b8%83%ef%bc%8c%e4%bd%a0%e8%bf%98%e5%ba%94%e8%af%a5%e7%9f%a5%e9%81%93%e5%a6%82%e4%bd%95%e7%94%a8%e4%bb%a3%e7%a0%81%e5%ae%9e%e7%8e%b0%ef%bc%81-%e9%9b%86","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=12729","title":{"rendered":"\u5173\u4e8e\u5e42\u5f8b\u5206\u5e03\uff0c\u4f60\u8fd8\u5e94\u8be5\u77e5\u9053\u5982\u4f55\u7528\u4ee3\u7801\u5b9e\u73b0\uff01| \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\"\u96c6\u667a\"<\/p>\n

\n
\u5bfc\u8bed<\/strong><\/p>\n
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\u5e42\u5f8b\u6982\u7387\u5206\u5e03<\/strong><\/p>\n

\uff08Power-law probability distributions\uff09<\/strong><\/p>\n

\u5e7f\u4e49\u4e0a\uff0c\u5e42\u5f8b\u6982\u7387\u5206\u5e03\u662f\u4e00\u4e2a\u5bc6\u5ea6\u51fd\u6570\uff08\u6216\u79bb\u6563\u60c5\u51b5\u4e0b\u7684\u6982\u7387\u8d28\u91cf\u51fd\u6570\uff09\u5177\u6709\u4ee5\u4e0b\u5f62\u5f0f\u7684\u5206\u5e03\uff1a \u5bf9\u4e8e\u8f83\u5927\u7684<\/span>\"\u96c6\u667a\"\uff0c<\/span>\"\u96c6\u667a\"\uff0c\u5176\u4e2d<\/span>\"\u96c6\u667a\"\u4e14<\/span>\"\u96c6\u667a\"\u662f\u4e00\u4e2a\u6162\u53d8\u51fd\u6570(Slowly varying function)\uff0c\u5bf9\u4e8e\u4efb\u4f55\u6b63\u56e0\u5b50<\/span>\"\u96c6\u667a\"\uff0c\u5b83\u90fd\u6ee1\u8db3<\/span>\"\u96c6\u667a\"\u7684\u8fd9\u4e2a\u5c5e\u6027\u6765\u81ea\u4e8e<\/span>\"\u96c6\u667a\"\u6e10\u8fdb\u7684\u6807\u5ea6\u4e0d\u53d8\u6027\u3002\u56e0\u6b64\uff0c<\/span>\"\u96c6\u667a\"\u4ec5\u63a7\u5236\u5de6\u5c3e\u7684\u5f62\u72b6\u548c\u6709\u9650\u8303\u56f4\u3002\u5982\u679c<\/span>\"\u96c6\u667a\"\u662f\u5e38\u91cf\u56e0\u5b50\u51fd\u6570\uff0c\u5e76\u4e14\u6211\u4eec\u6709\u4e00\u4e2a\u5e42\u5f8b\u9002\u7528\u4e8e\u6240\u6709\u7684<\/span>\"\u96c6\u667a\"\u503c\uff0c\u5728\u8bb8\u591a\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u4f9d\u636e\u5e42\u5f8b\u5047\u8bbe\u51fa\u4e00\u4e2a\u4e0b\u9650\u3002\u7ed3\u5408\u8fd9\u4e24\u79cd\u60c5\u51b5\uff0c\u5f53<\/span>\"\u96c6\u667a\"\u662f\u4e00\u4e2a\u8fde\u7eed\u53d8\u91cf\uff0c\u5e42\u5f8b\u6709\u4ee5\u4e0b\u5f62\u5f0f\uff1a<\/span>\"\u96c6\u667a\"<\/p>\n

\u5176\u4e2d\uff0c<\/span>\"\u96c6\u667a\"\u662f\u6807\u51c6\u5316\u5e38\u91cf\u56e0\u5b50<\/strong><\/span><\/p>\n

\u4e0b\u9762\u6211\u4eec\u6765\u8ba8\u8bba\u8fd9\u4e2a\u5206\u5e03\u7684\u6027\u8d28\u3002 \u9996\u5148\uff0c\u5b83\u7684\u77e9\u53ef\u8868\u793a\u4e3a\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u5f53<\/span>\"\u96c6\u667a\"\uff0c\u5b9a\u4e49\u662f\u5b8c\u5907\u7684\uff1b \u5f53<\/span>\"\u96c6\u667a\"\uff0c\u53d1\u6563\uff1a \u5f53<\/span>\"\u96c6\u667a\"\uff0c\u5747\u503c\u4e0e\u9ad8\u9636\u77e9\u90fd\u662f\u65e0\u7a77\u5927\uff1b \u5f53<\/span>\"\u96c6\u667a\"\uff0c\u5747\u503c\u5b58\u5728\uff0c\u4f46\u65b9\u5dee\u548c\u9ad8\u9636\u77e9\u90fd\u662f\u65e0\u7a77\u5927\u3002 \u5982\u679c\u4ece\u8fd9\u79cd\u5206\u5e03\u4e2d\u62bd\u53d6\u6709\u9650\u6837\u672c\uff0c\u610f\u5473\u7740\u4e2d\u5fc3\u77e9\u4f30\u8ba1\u6c38\u8fdc\u4e0d\u4f1a\u6536\u655b\u2014\u2014\u5e76\u4e14\u968f\u7740\u6570\u636e\u7684\u589e\u591a\uff0c\u4ed6\u4eec\u8fd8\u6709\u589e\u5927\u7684\u8d8b\u52bf\u3002\u8fd9\u79cd\u5e42\u5f8b\u6982\u7387\u5206\u5e03\u53c8\u88ab\u79f0\u4e3a\u5e15\u7d2f\u6258\u578b\u5206\u5e03\uff0c\u5177\u6709\u5e15\u7d2f\u6258\u5c3e\u90e8\u7279\u5f81\u7684\u5206\u5e03\uff0c\u6216\u662f\u5177\u6709\u89c4\u5219\u53d8\u5316\u7684\u5206\u5e03\u3002<\/strong><\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n

\u5e15\u7d2f\u6258\u578b\u5206\u5e03 |\u6765\u6e90\uff1ahttps:\/\/www.google.com<\/strong><\/p>\n

\u4e00\u79cd\u4e0d\u6ee1\u8db3\u4e0a\u9762\u7684\u4e00\u822c\u5f62\u5f0f\u7684\u4fee\u6539\uff0c\u5373\u6307\u6570\u622a\u6b62\u5e42\u5f8b\u5206\u5e03\u3002<\/strong><\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n

\u5728\u8fd9\u79cd\u5206\u5e03\u4e2d\uff0c\u6307\u6570\u8870\u51cf\u9879<\/span>\"\u96c6\u667a\"\u6700\u7ec8\u4f1a\u5728\u8f83\u5927\u7684\u5904\u8d85\u8fc7\u6b63\u5e38\u7684\u5e42\u5f8b\u5206\u5e03\u3002\u8fd9\u79cd\u5206\u5e03\u65e0\u6cd5\u6210\u6bd4\u4f8b\u7f29\u653e\uff0c\u56e0\u6b64\u5e76\u4e0d\u662f\u5e42\u5f8b;\u4e0d\u8fc7\uff0c\u5b83\u4f1a\u5728\u622a\u6b62\u524d\u7684\u6709\u9650\u533a\u57df\u5185\u8fd1\u4f3c\u5730\u7f29\u653e\u3002<\/span>\uff08\u6ce8\u610f\uff0c\u4e00\u822c\u7684\u5e42\u5f8b\u5206\u5e03\u662f\u8fd9\u79cd\u5206\u5e03\u7684\u7b80\u5355\u5f62\u5f0f\uff0c\u5373<\/span>\"\u96c6\u667a\"\u7684\u6307\u6570\u622a\u6b62\u5e42\u5f8b\u5206\u5e03\u3002\uff09<\/span><\/strong>\u8fd9\u79cd\u5206\u5e03\u662f\u6e10\u8fd1\u5e42\u5f8b\u5206\u5e03\u7684\u5e38\u89c1\u66ff\u4ee3\u65b9\u6cd5\uff0c\u56e0\u4e3a\u5b83\u8003\u8651\u4e86\u6709\u9650\u5927\u5c0f\u7684\u5f71\u54cd\u3002<\/span><\/p>\n

Tweedie\u5206\u5e03\u662f\u4e00\u65cf\u7edf\u8ba1\u6a21\u578b\uff0c\u5176\u7279\u5f81\u662f\u57fa\u4e8e\u53ef\u52a0\uff08additive\uff09\u4e0e\u53ef\u518d\u751f\uff08reproductive\uff09\u5377\u79ef\u4ee5\u53ca\u6807\u5ea6\u53d8\u6362\uff08scale transformation\uff09\u7684\u95ed\u5305\uff08closure\uff09\u3002<\/span><\/strong>\u56e0\u6b64\uff0c\u8fd9\u4e9b\u6a21\u578b\u90fd\u8868\u8fbe\u4e86\u65b9\u5dee\u548c\u5747\u503c\u4e4b\u95f4\u7684\u5e42\u5f8b\u5173\u7cfb\u3002\u8fd9\u4e9b\u6a21\u578b\u4f5c\u4e3a\u6570\u5b66\u6536\u655b\u7684\u7126\u70b9\uff0c\u7c7b\u4f3c\u4e8e\u6b63\u6001\u5206\u5e03\u5728\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u4e2d\u6240\u626e\u6f14\u7684\u89d2\u8272\u3002\u8fd9\u79cd\u6536\u655b\u6548\u5e94\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48\u5728\u81ea\u7136\u8fc7\u7a0b\u4e2d, \u65b9\u5dee-\u5e73\u5747\u5e42\u5f8b\u8868\u73b0\u5f97\u5982\u6b64\u5e7f\u6cdb, \u5c31\u50cf\u6cf0\u52d2\u5728\u751f\u6001\u5b66\u4e2d\u7684\u5b9a\u5f8b\u548c\u5728\u7269\u7406\u5b66\u4e2d\u7684\u6da8\u843d\u6807\u5ea6\u3002\u8fd8\u53ef\u4ee5\u8bc1\u660e\uff0c\u4f7f\u7528\u6269\u5c55\u7bb1\uff08 expanding bins\uff09\u7684\u65b9\u6cd5\u65f6\uff0c\u8fd9\u79cd\u65b9\u5dee- \u5747\u503c\u5e42\u5f8b\u5206\u5e03\uff08variance-to-mean power law\uff09\u610f\u5473\u7740\u5b58\u57281 \/f\u566a\u58f0\uff0c\u800c1\/ f\u566a\u58f0\u53ef\u80fd\u662f\u7531\u4e8eTweedie\u6536\u655b\u6548\u5e94\uff08Tweedie convergence effect\uff09\u800c\u4ea7\u751f\u7684\u3002<\/span><\/p>\n

\u56fe\u5f62\u9a8c\u8bc1\u6cd5<\/strong><\/p>\n

\u68c0\u9a8c\u5e42\u5f8b\u6982\u7387\u5206\u5e03<\/strong><\/p>\n

\u867d\u7136\u4eba\u4eec\u5df2\u7ecf\u63d0\u51fa\u4e86\u66f4\u6210\u719f\u66f4\u7a33\u5065\u7684\u65b9\u6cd5\uff0c\u4f46\u901a\u8fc7\u968f\u673a\u6837\u672c\u68c0\u9a8c\u5e42\u5f8b\u6982\u7387\u5206\u5e03\u7684\u6700\u5e38\u7528\u7684\u56fe\u5f62\u65b9\u6cd5\u8fd8\u662f\u5e15\u7d2f\u6258\u53cc\u5206\u4f4d\u56fe\uff08Pareto quantile-quantile plots \uff09\uff08\u6216\u5e15\u7d2f\u6258Q-Q\u56fe\uff09\uff0c\u5e73\u5747\u5269\u4f59\u5bff\u547d\u56fe\uff08mean residual life plot\uff09\u548c\u53cc\u5bf9\u6570\u56fe\uff08Paretoquantile-quantile plots\uff09\u3002<\/span><\/p>\n

 <\/p>\n

\"\u96c6\u667a\"<\/div>\n

\uff08log-log\u56fe\uff09<\/span><\/strong><\/p>\n

\u5728\u53cc\u5bf9\u6570\u56fe\u4e0a\u5448\u73b0\u76f4\u7ebf\u662f\u5fc5\u8981\u7684\uff0c\u4f46\u5e76\u6ca1\u6709\u8db3\u591f\u7684\u8bc1\u636e\u8bc1\u660e\u4ed6\u4eec\u7684\u5e42\u5f8b\u5173\u7cfb\uff0c\u76f4\u7ebf\u7684\u659c\u7387\u5c31\u5bf9\u5e94\u4e8e\u5e42\u5f8b\u6307\u6570\u3002<\/span><\/strong><\/p>\n

 <\/p>\n

\u53e6\u4e00\u79cd\u66f4\u5f3a\u5927\u7684\u56fe\u5f62\u68c0\u9a8c\u6cd5\u662f<\/span><\/strong>\u5229\u7528bundles of residual quantile functions \u6b8b\u4f59\u5206\u4f4d\u51fd\u6570\u675f\u3002\uff08\u6ce8\u610f\uff0c\u5e42\u5f8b\u5206\u5e03\u4e5f\u79f0\u4e3a\u5e15\u7d2f\u6258\u5206\u5e03\u3002\uff09<\/strong>\u8fd9\u91cc\u5047\u8bbe\u4ece\u6982\u7387\u5206\u5e03\u4e2d\u83b7\u5f97\u968f\u673a\u6837\u672c\uff0c\u5e76\u4e14\u6211\u4eec\u60f3\u77e5\u9053\u5206\u5e03\u7684\u5c3e\u90e8\u662f\u5426\u9075\u5faa\u5e42\u5f8b\uff08\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u60f3\u77e5\u9053\u5206\u5e03\u662f\u5426\u6709\u201c\u5e15\u7d2f\u6258\u5c3e\u201d\uff09\u3002\u6b64\u5904\u968f\u673a\u6837\u672c\u4e5f\u88ab\u79f0\u4e3a\u201c\u6570\u636e\u201d\u3002<\/span><\/p>\n

\u5e15\u7d2f\u6258Q-Q\u56fe<\/span><\/strong>\u662f\u8fd9\u6837\u7ed8\u5236\u7684\uff1a\u5b83\u5c06\u53d6\u5bf9\u6570\u540e\uff08\u6837\u672c\uff09\u6570\u636e\u7684\u5206\u4f4d\u6570\u4e0e\u53d6\u5747\u503c\u4e3a1\u7684\u6307\u6570\u5206\u5e03\u5bf9\u5e94\u7684\u5206\u4f4d\u6570\uff08\u6216\u6807\u51c6\u5e15\u7d2f\u6258\u5206\u5e03\u7684\u4f4d\u6570\uff09\u8fdb\u884c\u6bd4\u8f83\u3002\u5982\u679c\u5f97\u5230\u7684\u6563\u70b9\u56fe\u8868\u73b0\u662f\u201c\u6e10\u8fd1\u6536\u655b\u201d\u4e3a\u76f4\u7ebf\uff0c\u5c31\u5e94\u8be5\u6000\u7591\u5176\u670d\u4ece\u5e42\u5f8b\u5206\u5e03\u3002\u5e15\u7d2f\u6258 Q-Q\u56fe\u7684\u5c40\u9650\u662f\u5b83\u5728\u5c3e\u90e8\u6307\u6570\uff08\u4e5f\u79f0\u4e3a\u5e15\u7d2f\u6258\u6307\u6570\uff09\u63a5\u8fd1\u4e8e0\u65f6\u8868\u73b0\u4e0d\u4f73\uff0c\u56e0\u4e3a\u5e15\u7d2f\u6258Q-Q\u56fe\u96be\u4ee5\u68c0\u9a8c\u5c3e\u90e8\u662f\u7f13\u6162\u53d8\u5316\u7684\u5206\u5e03\u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/div>\n

\u5e15\u7d2f\u6258\u5206\u5e03 |\u6765\u6e90\uff1ahttps:\/\/www.google.com<\/span><\/strong><\/p>\n

\u53e6\u4e00\u79cd\u68c0\u9a8c\u5e42\u5f8b\u6982\u7387\u5206\u5e03\u7684\u65b9\u6cd5\u662f<\/span><\/strong>\u5e73\u5747\u5269\u4f59\u5bff\u547d\u56fe<\/strong>\uff0c\u5b83\u5305\u542b\u4ee5\u4e0b\u6b65\u9aa4\uff1a\u9996\u5148\u5bf9\u6570\u636e\u53d6\u5bf9\u6570\uff0c\u7136\u540e\u5c06\u9ad8\u4e8e\u7b2ci\u9636\u7edf\u8ba1\u91cf\u7684\u6570\u636e\u5e73\u5747\u503c\u4e0e\u7b2ci\u9636\u7edf\u8ba1\u91cf\u8fdb\u884c\u6bd4\u8f83\u7ed8\u5236\uff0c\u4ecei=1,…,n,\u5176\u4e2dn\u662f\u968f\u673a\u6837\u672c\u5bb9\u91cf\u3002\u5982\u679c\u7ed8\u5236\u51fa\u7684\u6563\u70b9\u56fe\u8d70\u52bf\u5448\u73b0\u4e3a\u4e00\u6761\u201c\u7a33\u5b9a\u201d\u7684\u6c34\u5e73\u76f4\u7ebf\uff0c\u90a3\u4e48\u5e94\u8be5\u8003\u8651\u5176\u670d\u4ece\u5e42\u5f8b\u5206\u5e03\u3002\u4f46\u7531\u4e8e\u5e73\u5747\u5269\u4f59\u5bff\u547d\u56fe\u5bf9\u5f02\u5e38\u503c\u975e\u5e38\u654f\u611f\uff08\u5b83\u5e76\u4e0d\u7a33\u5065\uff09\uff0c\u6240\u4ee5\u5b83\u901a\u5e38\u4f1a\u4ea7\u751f\u4e00\u4e9b\u96be\u4ee5\u89e3\u91ca\u7684\u56fe\u5f62;\u800c\u8fd9\u4e9b\u56fe\u5f62\u901a\u5e38\u88ab\u79f0\u4e3a Hill horror plots \u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/div>\n

Hill horror plots |\u6765\u6e90\uff1ahttps:\/\/www.google.com<\/span><\/strong><\/p>\n

\u53cc\u5bf9\u6570\u56fe\u662f\u4f7f\u7528\u968f\u673a\u6837\u672c\u4ee5\u56fe\u5f62\u65b9\u5f0f\u68c0\u9a8c\u5c3e\u90e8\u5206\u5e03\u7684\u53e6\u4e00\u79cd\u65b9\u5f0f\u3002<\/span><\/strong>\u4f7f\u7528\u8fd9\u4e2a\u65b9\u6cd5\u5fc5\u987b\u8981\u8c28\u614e\uff0c\u56e0\u4e3a\u53cc\u5bf9\u6570\u56fe\u4e2d\u5448\u73b0\u76f4\u7ebf\u5bf9\u5e42\u5f8b\u6982\u7387\u5206\u5e03\u662f\u5fc5\u8981\u4e0d\u5145\u5206\u6761\u4ef6\uff0c\u8bb8\u591a\u975e\u5e42\u5f8b\u5206\u5e03\u5728\u53cc\u5bf9\u6570\u56fe\u4e0a\u4e5f\u663e\u793a\u4e3a\u76f4\u7ebf\u3002\u8fd9\u4e2a\u65b9\u6cd5\u662f\u5c06\u7279\u5b9a\u6570\u5728\u8be5\u5206\u5e03\u4e2d\u7684\u6982\u7387\u4f30\u8ba1\u91cf\u7684\u5bf9\u6570 | \u5bf9\u6bd4\u8fd9\u4e2a\u6570\u7684\u5bf9\u6570 | \u8fdb\u884c\u7ed8\u56fe\u3002\u901a\u5e38\uff0c\u6b64\u4f30\u8ba1\u91cf\u662f\u8be5\u6570\u636e\u5728\u6570\u636e\u96c6\u4e2d\u51fa\u73b0\u7684\u6b21\u6570\u7684\u6bd4\u4f8b\u3002\u5982\u679c\u56fe\u4e2d\u7684\u70b9\u5728x\u8f83\u5927\u65f6\u503e\u5411\u4e8e\u201c\u6536\u655b\u201d\u4e3a\u76f4\u7ebf\uff0c\u5219\u53ef\u5f97\u51fa\u7ed3\u8bba\uff0c\u8be5\u5206\u5e03\u5177\u6709\u201c\u5e42\u5f8b\u5c3e\u201d\uff08power-law tail\uff09\u3002\u76ee\u524d\u8fd9\u4e9b\u7c7b\u578b\u7684\u7ed8\u56fe\u7684\u5e94\u7528\u793a\u4f8b\u5df2\u7ecf\u53d1\u8868\u3002\u4f46\u8fd9\u79cd\u65b9\u6cd5\u7684\u5c40\u9650\u662f\uff0c\u9700\u8981\u5927\u91cf\u7684\u6570\u636e\u624d\u80fd\u4f7f\u7ed3\u679c\u53ef\u9760\u3002\u6b64\u5916\uff0c\u5b83\u4ec5\u9002\u7528\u4e8e\u79bb\u6563\uff08\u6216\u5206\u7ec4\uff09\u6570\u636e\u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/div>\n

log-log Graph \u53cc\u5bf9\u6570\u66f2\u7ebf\u56fe | \u6765\u6e90\uff1ahttps:\/\/www.google.com<\/span><\/strong><\/p>\n

\u4e0d\u8fc7\uff0c\u76ee\u524d\u5df2\u7ecf\u63d0\u51fa\u4e86\u4f7f\u7528\u968f\u673a\u6837\u672c\u68c0\u9a8c\u5e42\u5f8b\u6982\u7387\u5206\u5e03\u7684\u53e6\u4e00\u79cd\u56fe\u5f62\u65b9\u6cd5\u3002\u8be5\u65b9\u6cd5\u5305\u62ec\u7ed8\u5236\u5bf9\u6570\u53d8\u6362\u6837\u672c\u7684\u675f\uff0c<\/strong>\u662f\u6700\u65e9\u63d0\u51fa\u4f7f\u7528\u968f\u673a\u6837\u672c\u63a2\u7d22\u77e9\u7684\u5b58\u5728\u548c\u77e9\u751f\u6210\u51fd\u6570\u7684\u5de5\u5177\uff0c\u57fa\u4e8e\u6b8b\u5dee\u5206\u4f4d\u51fd\u6570\uff08RQF\uff09\uff08\u4e5f\u79f0\u4e3a\u6b8b\u5dee\u767e\u5206\u4f4d\u51fd\u6570\uff09\uff0c\u5b83\u63d0\u4f9b\u4e86\u8bb8\u591a\u4f17\u6240\u5468\u77e5\u7684\u6982\u7387\u5206\u5e03\u7684\u5c3e\u90e8\u884c\u4e3a\u7684\u5b8c\u6574\u8868\u5f81\uff0c\u5305\u62ec\u5e42\u5f8b\u5206\u5e03\u4e0e\u5176\u4ed6\u7c7b\u578b\u7684\u91cd\u5c3e\uff0c\u751a\u81f3\u975e\u91cd\u5c3e\u5206\u5e03\u7684\u5206\u5e03\u3002\u8fd9\u79cd\u65b9\u6cd5\u7ed8\u5236\u7684\u56fe\u5f62\u6ca1\u6709\u4e0a\u9762\u63d0\u5230\u7684\u5e73\u5747\u5269\u4f59\u5bff\u547d\u56fe\u3001\u53cc\u5bf9\u6570\u56fe\u548c\u5e15\u7d2f\u6258 Q-Q\u56fe\u7684\u7f3a\u70b9\uff0c\u5b83\u4eec\u5bf9\u5f02\u5e38\u503c\u5f88\u654f\u611f\uff0c\u80fd\u591f\u76f4\u89c2\u5730\u68c0\u9a8c\u5177\u6709\u5c0f\u503c\u7684\u5e42\u5f8b\uff0c\u5e76\u4e14\u4e0d\u9002\u7528\u4e8e\u5206\u6790\u5927\u91cf\u6570\u636e\u3002\u6b64\u5916\uff0c\u5176\u4ed6\u5206\u5e03\u7c7b\u578b\u7684\u5c3e\u90e8\u4e5f\u53ef\u4ee5\u7528\u8fd9\u4e2a\u65b9\u6cd5\u89c2\u5bdf\u68c0\u9a8c\u3002<\/span><\/p>\n

\n

\n

\u7ed8\u5236\u5e42\u5f8b\u5206\u5e03<\/p>\n

\uff08Plotting power-law distributions\uff09<\/strong><\/p>\n

\u4e00\u822c\u6765\u8bf4\uff0c\u5e42\u5f8b\u5206\u5e03\u662f\u5728\u53cc\u5bf9\u6570\u5750\u6807\u8f74\u4e0a\u7ed8\u5236\u7684\uff0c\u5f3a\u8c03\u53f3\u5c3e\u90e8\u5206\u3002\u6700\u7b80\u4fbf\u76f4\u89c2\u7684\u65b9\u6cd5\u662f\u901a\u8fc7\uff08\u4e92\u8865\uff09\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\uff08cumulativedistribution function\uff0c\u7f29\u5199\u4e3acdf\uff09<\/strong>\u8bf4\u660e\uff1a<\/span>\"\u96c6\u667a\"\"\u96c6\u667a\"<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u7d2f\u79ef\u5206\u5e03\u51fd\u6570 |\u6765\u6e90\uff1ahttps:\/\/www.google.com<\/span><\/strong><\/p>\n

\u6ce8\u610f\uff0c<\/span><\/strong>cdf\u4e5f\u662f\u5e42\u5f8b\u51fd\u6570\uff0c\u53ea\u662f\u5b83\u7684\u6807\u5ea6\u6307\u6570\u8f83\u5c0f\u3002<\/strong>\u4ece\u6570\u636e\u5904\u7406\u89d2\u5ea6\uff0ccdf\u7684\u7b49\u4ef7\u5f62\u5f0f\u662frank-frequency \u5206\u5e03<\/strong>\uff0c\u5373\u5148\u6309\u5347\u5e8f\u6392\u5217\u7684\u89c2\u5bdf\u503c\uff0c\u518d\u5c06\u5b83\u4eec\u4e0e\u77e2\u91cf<\/span>\"\u96c6\u667a\"\u5bf9\u5e94\u3002<\/span><\/p>\n

\u5c3d\u7ba1\u4fbf\u4e8e\u8bb0\u5f55\u6570\u636e\uff0c\u6291\u6216\u662f\u4fbf\u4e8e\u62df\u5408\u5e73\u6ed1\u6982\u7387\u5bc6\u5ea6\uff08\u8d28\u91cf\uff09\u51fd\u6570\uff0c\u4f46\u8fd9\u4e9b\u65b9\u6cd5\u5728\u6570\u636e\u8868\u793a\u4e2d\u5f15\u5165\u4e86\u9690\u5f0f\u504f\u5dee\uff0c\u56e0\u6b64\u5e94\u8be5\u907f\u514d\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6240\u8ff0\u7684cdf\u6cd5\u5bf9\u5904\u7406\u8fd9\u4e9b\u9690\u5f0f\u504f\u5dee\u66f4\u7a33\u5065\uff08\u4f46\u5e76\u975e\u6ca1\u6709\u504f\u8bef\uff09\u5e76\u4e14\u4fdd\u7559\u4e86\u5728\u53cc\u5bf9\u6570\u56fe\u5f62\u4e0a\u7684\u7ebf\u6027\u7279\u5f81\u3002<\/span><\/p>\n

\n

\u867d\u7136\u5728\u540c\u65f6\u7528\u7ebf\u6027\u6700\u5c0f\u4e8c\u4e58\u6cd5\u62df\u5408\u5e42\u5f8b\u65f6\uff0c\u4f7f\u7528cdf\u7ed8\u5236\u4f18\u4e8epdf\uff08\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff09\uff0c\u4f46\u5176\u4e0d\u53ef\u907f\u514d\u5730\u5728\u6570\u5b66\u4e0a\u6709\u4e0d\u51c6\u786e\u6027\u3002\u56e0\u6b64\uff0c\u5728\u4f30\u8ba1\u5e42\u5f8b\u5206\u5e03\u7684\u6307\u6570\u65f6\uff0c\u5efa\u8bae\u4f7f\u7528\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u3002<\/span><\/p>\n

\n

\n

\u4ece\u7ecf\u9a8c\u6570\u636e\u4f30\u8ba1\u6307\u6570<\/p>\n

\u6709\u8bb8\u591a\u65b9\u6cd5\u53ef\u4ee5\u4f30\u7b97\u5e42\u5f8b\u5c3e\u90e8\u7684\u6807\u5ea6\u6307\u6570\u503c\uff0c\u4f46\u5e76\u975e\u6240\u6709\u65b9\u6cd5\u90fd\u80fd\u4ea7\u751f\u65e0\u504f\u4e14\u4e00\u81f4\u7684\u7ed3\u679c\u3002<\/span><\/strong>\u4e00\u4e9b\u6700\u53ef\u9760\u7684\u6280\u672f\u901a\u5e38\u57fa\u4e8e\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u3002\u66ff\u4ee3\u65b9\u6cd5\u901a\u5e38\u57fa\u4e8e\u53cc\u5bf9\u6570\u6982\u7387\uff0c\u53cc\u5bf9\u6570\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\u6216\u5bf9\u6570\u5206\u7ec4\u6570\u636e\u8fdb\u884c\u7ebf\u6027\u56de\u5f52\uff0c\u4f46\u662f\uff0c\u5e94\u8be5\u907f\u514d\u8fd9\u4e9b\u65b9\u6cd5\uff0c\u56e0\u4e3a\u5b83\u4eec\u90fd\u53ef\u80fd\u5bfc\u81f4\u5bf9\u6807\u5ea6\u7cfb\u6570\u7684\u5177\u6709\u663e\u8457\u504f\u8bef\u7684\u4f30\u8ba1\u3002<\/span><\/p>\n

\n

\u5173\u4e8e\u8fd9\u4e9b\u65b9\u6cd5\uff0c\u4ee5\u53ca\u80fd\u591f\u4f7f\u7528\u5b83\u4eec\u7684\u6761\u4ef6\uff0c\u53ef\u4ee5\u8fdb\u4e00\u6b65\u53d1\u73b0\uff0c\u8fd9\u7bc7\u6587\u7ae0\u5168\u9762\u800c\u8be6\u7ec6\u5730\u63d0\u4f9b\u4e86\u53ef\u7528\u7684\u4ee3\u7801\uff08Matlab\u3001Python\u3001R\u548cC++\uff09\u6765\u8bc4\u4f30\u548c\u6d4b\u8bd5\u5e42\u5f8b\u5206\u5e03\u7684\u8fc7\u7a0b\u3002<\/span><\/p>\n

\n

\u8be6\u7ec6\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n

# coding: utf-8<\/p>\n

\n

# # \u7528numpy\u751f\u62100\uff0c1\u4e4b\u95f4\u7684\u5e42\u5f8b\u5206\u5e03<\/p>\n

#<\/p>\n

# ### \u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u4e3a<\/p>\n

# f(x) = a*x^(a-1)<\/p>\n

a = 0.4<\/p>\n

# \u91c7\u6837\u6570\u91cf<\/p>\n

samples = 10000<\/p>\n

s = np.random.power(a, samples)<\/p>\n

\n

\n

# \u7ed8\u56fe\u5c55\u793a\u7ed3\u679c<\/p>\n

import matplotlib.pyplot as plt<\/p>\n

count, bins, ignored = plt.hist(s, bins=50)<\/p>\n

x = np.linspace(0, 1, 100)<\/p>\n

y = a*x**(a-1.)<\/p>\n

normed_y = samples*np.diff(bins)[0]*y<\/p>\n

plt.plot(x, normed_y)<\/p>\n

plt.show()<\/p>\n

\n

# # \u4f7f\u7528\u539f\u751f\u65b9\u6cd5\u751f\u62100\uff0c1\u4e4b\u95f4\u7684\u5e42\u5f8b\u5206\u5e03<\/p>\n

import math<\/p>\n

# \u5206\u5e03\u51fd\u6570\u7684\u53cd\u51fd\u6570<\/p>\n

def rev(x,a):<\/p>\n

return math.exp(math.log(x) \/ a)<\/p>\n

\n

# \u751f\u6210\u5206\u5e03<\/p>\n

s1 = []<\/p>\n

for i in range(samples):<\/p>\n

s1.append(rev(np.random.uniform(0,1),a))<\/p>\n

# \u7ed8\u56fe<\/p>\n

count, bins, ignored = plt.hist(s1,bins=50)<\/p>\n

x = np.linspace(0, 1, 100)<\/p>\n

y = a*x**(a-1.)<\/p>\n

normed_y = samples*np.diff(bins)[0]*y<\/p>\n

plt.plot(x, normed_y)<\/p>\n

plt.show()<\/p>\n

\n

# # \u7ebf\u6027\u62df\u5408\u751f\u6210\u7ed3\u679c<\/p>\n

# \u7edf\u8ba1\u4e0d\u540c\u533a\u95f4\u7684\u6570\u636e\u6570\u91cf<\/p>\n

divide_num = 100<\/p>\n

ys = np.zeros(divide_num)<\/p>\n

xs = np.linspace(0,1,divide_num)<\/p>\n

for i in range(len(s)):<\/p>\n

ys[int(s[i] * 100)] += 1<\/p>\n

\n

# \u4f7f\u7528sklearn\u5305\u4e2d\u7684\u56de\u5f52\u5de5\u5177<\/p>\n

from sklearn import linear_model<\/p>\n

# \u56de\u5f52<\/p>\n

x_log = np.log(xs)<\/p>\n

y_log = np.log(ys)<\/p>\n

#\u7ebf\u6027\u62df\u5408\u6570\u636e\u51c6\u5907<\/p>\n

X_para=[]<\/p>\n

Y_para=[]<\/p>\n

for x ,y in zip(x_log[1:],y_log[1:]):<\/p>\n

X_para.append([float(x)])<\/p>\n

Y_para.append(float(y))<\/p>\n

# \u4f7f\u7528sklearn\u7684\u7ebf\u6027\u62df\u5408\u51fd\u6570\u8fdb\u884c\u62df\u5408<\/p>\n

regr = linear_model.LinearRegression()<\/p>\n

regr.fit(X_para, Y_para)<\/p>\n

#<\/p>\n

plt.title(“fit the log data”)<\/p>\n

plt.scatter(x_log,y_log,color =”black”)<\/p>\n

plt.plot(X_para, regr.predict(X_para),color=’blue’,linewidth=3)<\/p>\n

plt.show()<\/p>\n

\n

\n

\u901a\u8fc7R\u51fd\u6570\u4f30\u8ba1\u6307\u6570, \u5e76\u7ed8\u5236\u53cc\u5bf9\u6570\u6570\u636e\u62df\u5408\u7ebf\uff1a<\/span><\/strong><\/p>\n

\n

\u8be6\u7ec6\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n

pwrdist <- function(u,…) {<\/p>\n

<\/pre>\n
# u is vector of event counts, e.g. how many<\/p>\n
# crimes was a given perpetrator charged for by the police<\/p>\n
fx <- table(u)<\/p>\n
i <- as.numeric(names(fx))<\/p>\n
y <- rep(0,max(i))<\/p>\n
y[i] <- fx<\/p>\n
m0 <\/span><– glm(y<\/span>~<\/span>log(<\/span>1<\/span>:<\/span>max<\/span>(i))<\/span>,<\/span>family<\/span>=<\/span>quasipoisson())<\/span><\/p>\n
print(summary(m0))<\/p>\n
sub <-<\/p>\n
paste(“s=”,round(m0$coef[2],2),”lambda=”,sum(u),”\/”,length(u))<\/p>\n
plot(i,fx,log=”xy”,xlab=”x”,sub=sub,ylab=”counts”,…)<\/p>\n
grid()<\/p>\n
lines(1:max(i),(fitted(m0)),type=”b”)<\/p>\n
return(m0)<\/p>\n
}<\/p>\n
\u5982\u679c\u4f60\u6709\u66f4\u597d\u7684\u4ee3\u7801\uff0c\u6b22\u8fce\u8d21\u732e\u5230\u96c6\u667a\u767e\u79d1\u4e0a\uff0c\u6216\u8005\u8054\u7cfb\u6211\u4eec\uff0c\u6210\u4e3a\u6211\u4eec\u7684\u5fd7\u613f\u8005\uff01<\/span><\/p>\n
\u70b9\u51fb\u300c\u7f16\u8f91\u300d\uff0c\u505a\u4e9b\u6539\u53d8\uff0c\u6309\u4e0b\u300c\u4fdd\u5b58\u300d\uff0c\u4f60\u5c06\u5f71\u54cd\u4e16\u754c\uff01<\/a><\/span><\/p>\n
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\u6765\u6e90\uff1a\u96c6\u667a\u767e\u79d1<\/p>\n
\u5730\u5740\uff1a<\/p>\n
http:\/\/wiki.swarma.net\/index.php?title=%E5%B9%82%E5%BE%8B%E5%88%86%E5%B8%83&variant=zh-hans<\/p>\n
\u7f16\u8f91\uff1a\u5b5f\u5a55<\/p>\n<\/blockquote>\n
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\u63a8\u8350\u9605\u8bfb<\/strong><\/p>\n
\u5e42\u5f8b\u4e0e\u89c4\u6a21\u8bfb\u4e66\u4f1a\u62db\u52df<\/a><\/span><\/strong><\/span><\/p>\n
\u89e3\u8bfb\u5e42\u5f8b\u5206\u5e03\u4e0e\u65e0\u6807\u5ea6\u7f51\u7edc<\/a><\/span><\/strong><\/span><\/p>\n
\u590d\u6742\u7cfb\u7edf\u5165\u95e8\u5fc5\u4fee\u8bfe\u2014\u2014\u5e42\u5f8b\u5206\u5e03<\/a><\/span><\/strong><\/span><\/p>\n
\u793e\u4ea4\u7f51\u7edc\u4e2d\u7684\u5e42\u5f8b\u5206\u5e03<\/strong><\/span><\/a><\/p>\n
\u70b9\u51fb\u300c\u7f16\u8f91\u300d\uff0c\u505a\u4e9b\u6539\u53d8\uff0c\u6309\u4e0b\u300c\u4fdd\u5b58\u300d\uff0c\u4f60\u5c06\u5f71\u54cd\u4e16\u754c\uff01<\/strong><\/span><\/a><\/p>\n
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\u63a8\u8350\u8bfe\u7a0b<\/strong><\/p>\n
\"\u96c6\u667a\"<\/p>\n
\n
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\"\u96c6\u667a\"<\/div>\n
\n
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\u96c6\u667a\u4ff1\u4e50\u90e8QQ\u7fa4\uff5c877391004<\/strong><\/span><\/p>\n
\u5546\u52a1\u5408\u4f5c\u53ca\u6295\u7a3f\u8f6c\u8f7d\uff5cswarma@swarma.org<\/strong><\/span><\/p>\n
\n
\u25c6\u25c6\u25c6<\/strong><\/strong><\/span><\/h1>\n<\/section>\n
\u641c\u7d22\u516c\u4f17\u53f7\uff1a\u96c6\u667a\u4ff1\u4e50\u90e8<\/strong><\/p>\n
 <\/p>\n
\u52a0\u5165\u201c\u6ca1\u6709\u56f4\u5899\u7684\u7814\u7a76\u6240\u201d<\/span><\/strong><\/p>\n
\"\u96c6\u667a\"<\/p>\n<\/section>\n
\u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\u539f\u6587\u59cb\u53d1\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7\uff08 \u96c6\u667a\u4ff1\u4e50\u90e8 \uff09\uff1a\u96c6\u667a<\/a><\/p><\/blockquote>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
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