{"id":497,"date":"2023-07-29T17:25:02","date_gmt":"2023-07-29T17:25:02","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e7%82%b9%e4%bc%b0%e8%ae%a1%e8%ae%a1%e7%ae%97%e5%99%a8\/"},"modified":"2023-07-29T17:25:02","modified_gmt":"2023-07-29T17:25:02","slug":"%e7%82%b9%e4%bc%b0%e8%ae%a1%e8%ae%a1%e7%ae%97%e5%99%a8","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e7%82%b9%e4%bc%b0%e8%ae%a1%e8%ae%a1%e7%ae%97%e5%99%a8\/","title":{"rendered":"\u79ef\u5206\u4f30\u7b97\u8ba1\u7b97\u5668"},"content":{"rendered":"<p><script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjs\/5.1.1\/math.js\"><\/script><script src=\"https:\/\/cdn.jsdelivr.net\/npm\/jstat@latest\/dist\/jstat.min.js\"><\/script><\/p>\n<style>\n@import url('https:\/\/fonts.googleapis.com\/css?family=Droid+Serif|Raleway');<\/p>\n<p>.axis--y .domain {\n  display: none;\n}<\/p>\n<p>h1 {\ncolor: black;\ntext-align: center;\nmargin-top: 15px;\nmargin-bottom: 0px;\nfont-family: 'Raleway', sans-serif;\n}<\/p>\n<p>h2 {\ncolor: black;\nfont-size: 20px;\ntext-align: center;\nmargin-bottom: 15px;\nmargin-top: 15px;\nfont-family: 'Raleway', sans-serif;\n}<\/p>\n<p>p {\ncolor: black;\ntext-align: center;\nmargin-bottom: 15px;\nmargin-top: 15px;\nfont-family: 'Raleway', sans-serif;\n}<\/p>\n<p>#words_intro {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#words_outro {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#words {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 100px;\n}<\/p>\n<p>#calcTitle {\ntext-align: center;\nfont-size: 20px;\nmargin-bottom: 0px;\nfont-family: 'Raleway', serif;\n}<\/p>\n<p>#hr_top {\nwidth: 30%;\nmargin-bottom: 0px;\nmargin-top: 10px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>#hr_bottom {\nwidth: 30%;\nmargin-top: 15px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>.input_label_calc {\n    display: inline-block;\n    vertical-align: baseline;\n    width: 350px;\n}<\/p>\n<p>    #button_calc {\n      border: 1px solid;\n      border-radius: 10px;\n      margin-top: 20px;\n      padding: 10px 10px;\n      cursor: pointer;\n      outline: none;\n      background-color: white;\n      color: black;\n      font-family: 'Work Sans', sans-serif;\n      border: 1px solid grey;\n      \/* Green *\/\n    }<\/p>\n<p>    #button_calc:hover {\n      background-color: #f6f6f6;\n      border: 1px solid black;\n    }<\/p>\n<p>\t    .label_radio {\n\ttext-align: center;\n}\n<\/style>\n<div id=\"words_intro\"><b>\u70b9\u4f30\u8ba1<\/b>\u4ee3\u8868\u6211\u4eec\u5bf9\u603b\u4f53\u53c2\u6570\u7684\u201c\u6700\u4f73\u4f30\u8ba1\u201d\u3002<\/div>\n<div id=\"words_intro\">\u4f8b\u5982\uff0c\u6837\u672c\u5e73\u5747\u503c\u53ef\u4ee5\u7528\u4f5c\u603b\u4f53\u5e73\u5747\u503c\u7684\u70b9\u4f30\u8ba1\u3002<\/div>\n<div id=\"words_intro\">\u7c7b\u4f3c\u5730\uff0c\u6837\u672c\u6bd4\u4f8b\u53ef\u4ee5\u7528\u4f5c\u603b\u4f53\u6bd4\u4f8b\u7684\u70b9\u4f30\u8ba1\u3002\u4f46\u662f\uff0c\u6709\u591a\u79cd\u65b9\u6cd5\u53ef\u4ee5\u8ba1\u7b97\u4eba\u53e3\u6bd4\u4f8b\u7684\u70b9\u4f30\u8ba1\uff0c\u5305\u62ec\uff1a<\/div>\n<div id=\"words_intro\"><b>\u4f30\u8ba1 MLE \u70b9<\/b>\uff1ax \/ n<\/div>\n<div id=\"words_intro\"><b>\u4f30\u8ba1\u5a01\u5c14\u900a\u70b9<\/b>\uff1a(x + z <sup>2<\/sup> \/2) \/ (n + z <sup>2<\/sup> )<\/div>\n<div id=\"words_intro\"><b>\u6770\u5f17\u91cc\u70b9\u4f30\u8ba1<\/b>\uff1a(x + 0.5) \/ (n + 1)<\/div>\n<div id=\"words_intro\"><b>\u62c9\u666e\u62c9\u65af\u70b9\u7684\u4f30\u8ba1<\/b>\uff1a(x + 1) \/ (n + 2)<\/div>\n<div id=\"words_intro\">\u5176\u4e2d<b>x<\/b>\u662f\u6837\u672c\u4e2d\u7684\u201c\u547d\u4e2d\u201d\u6570\uff0c <b>n<\/b>\u662f\u6837\u672c\u5927\u5c0f\u6216\u8bd5\u9a8c\u6b21\u6570\uff0c <b>z<\/b>\u662f\u4e0e\u7f6e\u4fe1\u6c34\u5e73\u76f8\u5173\u7684 z \u5206\u6570\u3002<\/div>\n<div id=\"words_intro\">\u8981\u627e\u5230\u6700\u4f73\u70b9\u4f30\u8ba1\uff0c\u53ea\u9700\u5728\u4e0b\u9762\u7684\u6846\u4e2d\u8f93\u5165\u6210\u529f\u6b21\u6570\u3001\u8bd5\u9a8c\u6b21\u6570\u548c\u7f6e\u4fe1\u5ea6\u7684\u503c\uff0c\u7136\u540e\u5355\u51fb\u201c\u8ba1\u7b97\u201d\u6309\u94ae\u5373\u53ef\u3002<\/div>\n<div id=\"words\"><label class=\"input_label_calc\" for=\"x\"><b>\u6210\u529f\u6b21\u6570 (x)<\/b><\/label><input class=\"input_label_calc\" type=\"number\" id=\"x\" value=\"14\"><label class=\"input_label_calc\" for=\"n\"><b>\u8bd5\u9a8c\u6b21\u6570 (n)<\/b><\/label><input class=\"input_label_calc\" type=\"number\" id=\"n\" value=\"31\"><label class=\"input_label_calc\" for=\"conf\"><b>\u7f6e\u4fe1\u5ea6 (%)<\/b><\/label> <input class=\"input_label_calc\" type=\"number\" id=\"conf\" value=\"95\"><\/div>\n<div id=\"words\"><input class=\"input_label_calc\" type=\"button\" id=\"button_calc\" onclick=\"calc()\" value=\"Calculate\"><\/div>\n<div id=\"words_outro\">\n<p>\u6700\u4f73\u4f30\u8ba1 = <b><span id=\"best\">0.45695<\/span><\/b><\/p>\n<p>\u4f30\u8ba1 MLE \u70b9 = <span id=\"mle\">0.45161<\/span><\/p>\n<p>\u4f30\u8ba1\u5a01\u5c14\u900a\u70b9 = <span id=\"wilson\">0.45695<\/span><\/p>\n<p>\u6770\u5f17\u91cc\u70b9\u4f30\u8ba1 = <span id=\"jeffrey\">0.45313<\/span><\/p>\n<p>\u4f30\u8ba1\u62c9\u666e\u62c9\u65af\u70b9 = <span id=\"laplace\">0.45455<\/span><\/p>\n<\/div>\n<hr>\n<div id=\"words_intro\">\u8be5\u8ba1\u7b97\u5668\u4f7f\u7528\u4ee5\u4e0b\u903b\u8f91\u6765\u786e\u5b9a\u6700\u597d\u4f7f\u7528\u54ea\u4e2a\u70b9\u4f30\u8ba1\uff1a<\/div>\n<div id=\"words_intro\">\u5982\u679c<b>x\/n \u2264 0.5<\/b> \uff0c\u5219\u4f7f\u7528\u5a01\u5c14\u900a\u70b9\u4f30\u8ba1\u3002<\/div>\n<div id=\"words_intro\">\u5426\u5219\uff0c\u5982\u679c<b>x\/n &lt; 0.9<\/b> \uff0c\u5219\u4f7f\u7528 MLE \u70b9\u4f30\u8ba1\u3002<\/div>\n<div id=\"words_intro\">\u5426\u5219\uff0c\u5982\u679c<b>x\/n &lt; 1.0<\/b> \uff0c\u5219\u4f7f\u7528\u6770\u5f17\u91cc\u70b9\u6216\u62c9\u666e\u62c9\u65af\u70b9\u4f30\u8ba1\u4e2d\u8f83\u5c0f\u7684\u4e00\u4e2a\u3002<\/div>\n<div id=\"words_intro\">\u5426\u5219\uff0c\u5982\u679c<b>x\/n = 1.0<\/b> \uff0c\u5219\u4f7f\u7528\u62c9\u666e\u62c9\u65af\u70b9\u4f30\u8ba1\u3002<\/div>\n<p><script><\/p>\n<p>function calc() {\t<\/p>\n<p>\/\/get input values\nvar x = document.getElementById('x').value*1;\nvar n = document.getElementById('n').value*1;\nvar conf = (1 - document.getElementById('conf').value\/100)\/2;\nvar z = Math.abs(jStat.normal.inv(conf, 0, 1));<\/p>\n<p>\/\/find estimates\nvar mle = x\/n;\nvar wilson = (x - ((-z*z)\/2)) \/ (n - (-z*z));\nvar jeffrey = (x - (-.5)) \/ (n - (-1));\nvar laplace = (x - (-1)) \/ (n - (-2));<\/p>\n<p>\/\/find best estimate\nvar val = x\/n;\nvar best = x\/n;\nif (val <= 0.5) {\n  best = 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