{"id":25283,"date":"2021-04-04T16:55:00","date_gmt":"2021-04-04T08:55:00","guid":{"rendered":"https:\/\/swarma.org\/?p=25283"},"modified":"2021-04-04T16:55:00","modified_gmt":"2021-04-04T08:55:00","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e9%87%8d%e5%b0%be%e5%88%86%e5%b8%83-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=25283","title":{"rendered":"\u4ec0\u4e48\u662f\u91cd\u5c3e\u5206\u5e03 | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
\n

<\/p>\n


<\/p>\n

\u201c\u96c6\u667a\u767e\u79d1\u7cbe\u9009\u201d\u662f\u4e00\u4e2a\u957f\u671f\u4e13\u680f\uff0c\u6301\u7eed\u4e3a\u5927\u5bb6\u63a8\u9001\u590d\u6742\u6027\u79d1\u5b66\u76f8\u5173\u7684\u57fa\u672c\u6982\u5ff5\u548c\u8d44\u6e90\u4fe1\u606f\u3002\u4f5c\u4e3a\u96c6\u667a\u4ff1\u4e50\u90e8\u7684\u5f00\u6e90\u79d1\u5b66\u9879\u76ee\uff0c\u96c6\u667a\u767e\u79d1\u5e0c\u671b\u6253\u9020\u590d\u6742\u6027\u79d1\u5b66\u9886\u57df\u6700\u5168\u9762\u7684\u767e\u79d1\u5168\u4e66\uff0c\u6b22\u8fce\u5bf9\u590d\u6742\u6027\u79d1\u5b66\u611f\u5174\u8da3\u3001\u70ed\u7231\u77e5\u8bc6\u6574\u7406\u548c\u5206\u4eab\u7684\u670b\u53cb\u52a0\u5165\uff01
<\/span><\/section>\n

<\/section>\n
\u672c\u6587\u662f\u5bf9\u96c6\u667a\u767e\u79d1\u4e2d\u201c\u91cd\u5c3e\u5206\u5e03\u201d\u8bcd\u6761\u90e8\u5206\u5185\u5bb9\u7684\u6458\u5f55\uff0c\u53c2\u8003\u8d44\u6599\u53ca\u76f8\u5173\u8bcd\u6761\u8bf7\u53c2\u9605\u767e\u79d1\u8bcd\u6761\u539f\u6587\u3002<\/span><\/section>\n

<\/section>\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n

\u672c\u8bcd\u6761\u7531\u96c6\u667a\u4ff1\u4e50\u90e8\u4f17\u5305\u751f\u4ea7\uff0c\u96be\u514d\u5b58\u5728\u7eb0\u6f0f\u548c\u95ee\u9898\uff0c\u6b22\u8fce\u5927\u5bb6\u7559\u8a00\u53cd\u9988\u6216\u8005\u524d\u5f80\u5bf9\u5e94\u7684\u767e\u79d1\u8bcd\u6761\u9875\u9762\u8fdb\u884c\u4fee\u6539\uff0c\u4e00\u7ecf\u4fee\u6539\uff0c\u53ef\u4ee5\u83b7\u5f97\u5bf9\u5e94\u7684\u79ef\u5206\u5956\u52b1\u5662\uff01<\/em><\/span><\/p>\n


<\/p>\n

\n
\n
\n
\n
\n
\n
\n
\n
\n
\n

\u76ee\u5f55<\/strong><\/p>\n


<\/p>\n

\n
\u4e00\u3001\u5b9a\u4e49<\/span><\/strong><\/section>\n
\u4e8c\u3001\u5e38\u89c1\u7684\u91cd\u5c3e\u5206\u5e03<\/span><\/strong><\/section>\n
\u4e09\u3001\u4e0e\u80d6\u5c3e\u5206\u5e03\u7684\u5173\u7cfb
<\/span><\/strong><\/section>\n
\u56db\u3001\u91cd\u5c3e\u5bc6\u5ea6\u7684\u4f30\u8ba1<\/span><\/strong><\/section>\n
\u4e94\u3001\u7f16\u8005\u63a8\u8350
<\/span><\/strong><\/section>\n
\u516d\u3001\u96c6\u667a\u767e\u79d1\u8bcd\u6761\u5fd7\u613f\u8005\u62db\u52df<\/strong><\/strong><\/strong><\/span><\/strong><\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
<\/section>\n

\u5728\u6982\u7387\u8bba\u4e2d\uff0c\u91cd\u5c3e\u5206\u5e03 Heavy-tailed distributions\u662f\u6307\u5176\u5c3e\u90e8\u5448\u73b0\u51fa\u4e0d\u53d7\u6307\u6570\u9650\u5236\u7684\u6982\u7387\u5206\u5e03\uff1a\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u4eec\u7684\u5c3e\u90e8\u6bd4\u6307\u6570\u5206\u5e03 exponential distribution \u201c\u91cd\u201d\u3002\u5728\u8bb8\u591a\u5e94\u7528\u4e2d\uff0c\u5173\u6ce8\u7684\u662f\u5206\u5e03\u7684\u53f3\u5c3e\uff0c\u4f46\u662f\u5206\u5e03\u7684\u5de6\u5c3e\u53ef\u80fd\u4e5f\u5f88\u91cd\uff0c\u6216\u8005\u4e24\u4e2a\u5c3e\u90fd\u5f88\u91cd\u3002<\/span>
<\/p>\n


<\/p>\n

\u91cd\u5c3e\u5206\u5e03\u6709\u4e09\u4e2a\u91cd\u8981\u7684\u5b50\u7c7b\uff1a\u80d6\u5c3e\u5206\u5e03 Fat-tailed distribution\uff0c\u957f\u5c3e\u5206\u5e03 Long-tailed distribution\u548c\u6b21\u6307\u6570\u5206\u5e03 Subexponential distributions\u3002\u5b9e\u9645\u4e0a\uff0c\u6240\u6709\u5e38\u7528\u7684\u91cd\u5c3e\u5206\u5e03\u90fd\u5c5e\u4e8e\u6b21\u6307\u6570\u5206\u5e03\u7c7b subexponential class \u3002<\/span><\/p>\n


<\/p>\n

\u5728\u4f7f\u7528\u201c\u91cd\u5c3e\u201d Heavy-tailed\u4e00\u8bcd\u65f6\u4ecd\u5b58\u5728\u4e00\u4e9b\u6b67\u4e49\u3002\u4e8e\u662f\u5c31\u51fa\u73b0\u4e86\u53e6\u5916\u4e24\u79cd\u5b9a\u4e49\u3002<\/span><\/p>\n

\u6709\u4e00\u4e9b\u4f5c\u8005\u4f7f\u7528\u8be5\u672f\u8bed\u6765\u6307\u4ee3\u5e76\u975e\u6240\u6709\u9636\u77e9\u90fd\u662f\u6709\u9650\u7684\u90a3\u4e9b\u5206\u5e03\uff0c\u4e5f\u6709\u4e00\u4e9b\u4f5c\u8005\u4f7f\u7528\u8fd9\u4e2a\u672f\u8bed\u6765\u6307\u4ee3\u90a3\u4e9b\u6ca1\u6709\u6709\u9650\u65b9\u5dee\u7684\u5206\u5e03\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5728\u8fd9\u91cc\uff0c\u7ed9\u51fa\u7684\u662f\u6700\u5e38\u7528\u7684\u5b9a\u4e49\uff0c\u5305\u62ec\u5176\u4ed6\u5b9a\u4e49\u6240\u6db5\u76d6\u7684\u6240\u6709\u5206\u5e03\uff0c\u4ee5\u53ca\u5177\u6709\u6240\u6709\u5e42\u77e9\u4f46\u901a\u5e38\u88ab\u8ba4\u4e3a\u662f\u91cd\u5c3e\u5206\u5e03\u7684\u5bf9\u6570\u6b63\u6001\u5206\u5e03 long-normal distributions \u3002\uff08\u6709\u65f6\u201c\u91cd\u5c3e\u201d\u7528\u4e8e\u4efb\u4f55\u5177\u6709\u6bd4\u6b63\u6001\u5206\u5e03\u66f4\u91cd\u7684\u5c3e\u5df4\u7684\u5206\u5e03\u3002\uff09<\/span><\/p>\n

\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

\u5b9a\u4e49<\/span><\/strong><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n
<\/strong>
<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/p>\n

\u91cd\u5c3e\u5206\u5e03\u7684\u5b9a\u4e49<\/span><\/strong><\/h3>\n

\u5982\u679c X \u7684\u77e9\u6bcd\u51fd\u6570\uff0cMx(t)\u5bf9\u4e8e\u6240\u6709 t>0\u90fd\u662f\u65e0\u9650\u7684\uff0c\u5219\u5177\u6709\u5206\u5e03\u51fd\u6570 F \u7684\u968f\u673a\u53d8\u91cf \u7684\u5206\u5e03\u88ab\u79f0\u4e3a\u91cd\u5c3e\uff08\u53f3\uff09\u3002<\/span><\/p>\n

<\/p>\n

\u4e5f\u53ef\u4ee5\u5199\u6210\u5c3e\u5206\u5e03\u51fd\u6570 the tail distribution function \uff1a<\/span>
<\/p>\n

<\/p>\n

\u957f\u5c3e\u5206\u5e03\u7684\u5b9a\u4e49<\/span><\/h3>\n

\u5206\u5e03\u51fd\u6570\u4e3a<\/span> F \u7684\u968f\u673a\u53d8\u91cf<\/span> X \u5177\u6709\u957f\u5c3e\u5206\u5e03\uff0c\u5982\u679c\u5bf9\u4e8e\u6240\u6709 <\/span>t>0\uff0c\u90fd\u6ee1\u8db3<\/span><\/span><\/p>\n

<\/p>\n

\u6216\u7b49\u4ef7\u4e8e<\/span>
<\/p>\n

<\/section>\n

\u5bf9\u4e8e\u53f3\u5c3e\u957f\u5c3e\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u6709\u4e00\u4e2a\u76f4\u89c2\u7684\u89e3\u91ca\uff0c\u5373\u5728\u957f\u5c3e\u5206\u5e03\u968f\u673a\u53d8\u91cf\u5c3e\u90e8\u53d6\u503c\u5df2\u8d85\u8fc7\u67d0\u4e2a\u9ad8\u6c34\u5e73\u7684\u6761\u4ef6\u4e0b\uff0c\u5b83\u5c06\u8d85\u8fc7\u5176\u4ed6\u66f4\u9ad8\u6c34\u5e73\u7684\u6982\u7387\u63a5\u8fd1\u4e8e1\u3002<\/span><\/p>\n


\u6240\u6709\u957f\u5c3e\u5206\u5e03\u90fd\u662f\u91cd\u5c3e\u5206\u5e03\uff0c\u4f46\u53cd\u8fc7\u6765\u4e0d\u4e00\u5b9a\u6210\u7acb\uff0c\u4e14\u53ef\u4ee5\u6784\u9020\u51fa\u975e\u957f\u5c3e\u5206\u5e03\u7684\u91cd\u5c3e\u5206\u5e03\u3002<\/span><\/p>\n

\u6b21\u6307\u6570\u5206\u5e03<\/span><\/h3>\n

\u6b21\u6307\u6570\u6027\u662f\u6839\u636e\u6982\u7387\u5206\u5e03\u7684\u5377\u79ef Convolution \u5b9a\u4e49\u7684\u3002\u5bf9\u4e8e\u5177\u6709\u5171\u540c\u5206\u5e03\u51fd\u6570 F \u7684\u4e24\u4e2a\u72ec\u7acb\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf X1,X2, F\u4e0e\u81ea\u8eab\u7684\u5377\u79ef\uff0cF*2\u662f\u4e8c\u91cd\u5377\u79ef\uff0c\u4f7f\u7528Lebesgue\u2013Stieltjes\u79ef\u5206\uff0c\u65b9\u6cd5\u5982\u4e0b\uff1a<\/span><\/p>\n

<\/p>\n

\u5982\u679c\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff0c\u5206\u5e03 F \u5728\u6b63\u534a\u8f74\u4e0a\u662f\u4e3a\u6b21\u6307\u6570\u7684<\/span><\/p>\n

<\/p>\n

\u8fd9\u610f\u5473\u7740<\/span>\uff0c\u5bf9\u4e8e\u4efb\u4f55<\/span> n>=1\uff0c<\/span><\/p>\n

<\/p>\n

\u5bf9\u6b64\u7684\u6982\u7387\u89e3\u91ca\u662f\uff0c\u5bf9\u4e8e\u5177\u6709\u5171\u540c\u5206\u5e03 F \u7684 n \u4e2a\u72ec\u7acb\u968f\u673a\u53d8\u91cf X1,….,Xn \u7684\u603b\u548c<\/span><\/p>\n

<\/p>\n

\u8fd9\u901a\u5e38\u88ab\u79f0\u4e3a\u5355\u8df3 single big jump\u6216\u7a81\u53d8\u7406\u8bba catastrophe principle \u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5982\u679c\u5206\u5e03 FI([0,\u221e))\u4e3a\u5b9e\u6570\uff0c\u5219 F\u4e3a\u6574\u4e2a\u5b9e\u6570\u4e0a\u7684\u6b21\u6307\u6570\u5206\u5e03\u3002\u6b64\u65f6 I([0,\u221e))\u662f\u6b63\u534a\u8f74\u7684\u793a\u6027\u51fd\u6570\u3002\u6216\u8005\uff0c\u5f53\u4e14\u4ec5\u5f53 X^+=Max(0\uff0cX)\u662f\u6b21\u6307\u6570\u65f6\uff0c\u5219\u652f\u6491\u96c6\u4e3a\u5b9e\u6570\u8f74\u7684\u968f\u673a\u53d8\u91cf X \u662f\u6b21\u6307\u6570\u7684\u3002<\/span><\/p>\n


<\/p>\n

\u6240\u6709\u6b21\u6307\u6570\u5206\u5e03\u90fd\u662f\u957f\u5c3e\u5206\u5e03\uff0c\u4f46\u53ef\u4ee5\u6784\u9020\u51fa\u975e\u6b21\u6307\u6570\u5206\u5e03\u7684\u957f\u5c3e\u5206\u5e03\u7684\u793a\u4f8b\u3002<\/span><\/p>\n

\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

\u5e38\u89c1\u7684\u91cd\u5c3e\u5206\u5e03<\/span><\/strong><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n
<\/strong>
<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/p>\n

\u6240\u6709\u5e38\u7528\u7684\u91cd\u5c3e\u5206\u5e03\u90fd\u662f\u6b21\u6307\u6570\u7684\u3002<\/span><\/p>\n

\u5355\u5c3e\u7684\u5305\u62ec\uff1a<\/span><\/strong><\/p>\n

    \n
  • \n

    \u5e15\u7d2f\u6258\u5206\u5e03 Pareto distribution;<\/span><\/p>\n<\/li>\n

  • \n

    \u5bf9\u6570\u6b63\u6001\u5206\u5e03 Log-normal distribution;<\/span><\/p>\n<\/li>\n

  • \n

    \u83b1\u7ef4\u5206\u5e03 L\u00e9vy distribution;<\/span><\/p>\n<\/li>\n

  • \n

    \u5f62\u72b6\u53c2\u6570\u5927\u4e8e0\u4f46\u5c0f\u4e8e1\u7684\u97e6\u5e03\u5c14\u5206\u5e03 Weibull distribution;<\/span><\/p>\n<\/li>\n

  • \n

    \u4f2f\u5c14\u5206\u5e03 Burr distribution;<\/span><\/p>\n<\/li>\n

  • \n

    \u5bf9\u6570\u903b\u8f91\u5206\u5e03 log-logistic distribution;<\/span><\/p>\n<\/li>\n

  • \n

    \u5bf9\u6570\u4f3d\u739b\u5206\u5e03 log-gamma distribution;<\/span><\/p>\n<\/li>\n

  • \n

    \u5f17\u96f7\u6b47\u5206\u5e03 Fr\u00e9chet distribution;<\/span><\/p>\n<\/li>\n

  • \n

    \u5bf9\u6570\u67ef\u897f\u5206\u5e03 log-Cauchy distribution\uff0c\u6709\u65f6\u88ab\u63cf\u8ff0\u4e3a\u201c\u8d85\u91cd\u5c3e\u201d\u5206\u5e03\uff0c\u56e0\u4e3a\u5b83\u8868\u73b0\u51fa\u5bf9\u6570\u8870\u51cf\uff0c\u4ece\u800c\u4ea7\u751f\u6bd4\u5e15\u7d2f\u6258\u5206\u5e03\u66f4\u91cd\u7684\u5c3e\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n

    \u53cc\u5c3e\u7684\u5305\u62ec\uff1a<\/span><\/strong><\/p>\n