{"id":495,"date":"2023-07-29T17:25:02","date_gmt":"2023-07-29T17:25:02","guid":{"rendered":"https:\/\/statorials.org\/my\/%e1%80%a1%e1%80%99%e1%80%be%e1%80%90%e1%80%ba%e1%80%81%e1%80%94%e1%80%b7%e1%80%ba%e1%80%99%e1%80%be%e1%80%94%e1%80%ba%e1%80%b8%e1%80%82%e1%80%8f%e1%80%94%e1%80%ba%e1%80%b8%e1%80%90%e1%80%bd%e1%80%80\/"},"modified":"2023-07-29T17:25:02","modified_gmt":"2023-07-29T17:25:02","slug":"%e1%80%a1%e1%80%99%e1%80%be%e1%80%90%e1%80%ba%e1%80%81%e1%80%94%e1%80%b7%e1%80%ba%e1%80%99%e1%80%be%e1%80%94%e1%80%ba%e1%80%b8%e1%80%82%e1%80%8f%e1%80%94%e1%80%ba%e1%80%b8%e1%80%90%e1%80%bd%e1%80%80","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/%e1%80%a1%e1%80%99%e1%80%be%e1%80%90%e1%80%ba%e1%80%81%e1%80%94%e1%80%b7%e1%80%ba%e1%80%99%e1%80%be%e1%80%94%e1%80%ba%e1%80%b8%e1%80%82%e1%80%8f%e1%80%94%e1%80%ba%e1%80%b8%e1%80%90%e1%80%bd%e1%80%80\/","title":{"rendered":"\u1021\u1019\u103e\u1010\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a"},"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 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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>\u1021\u1019\u103e\u1010\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u101e\u100a\u103a<\/b> \u101c\u1030\u1026\u1038\u101b\u1031\u1000\u1014\u1037\u103a\u101e\u1010\u103a\u1001\u103b\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u104f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f &#8220; \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a&#8221;  \u1000\u102d\u102f \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/div>\n<div id=\"words_intro\"> \u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1014\u1019\u1030\u1014\u102c\u1006\u102d\u102f\u101c\u102d\u102f\u1021\u102c\u1038 \u101c\u1030\u1026\u1038\u101b\u1031\u1010\u1005\u103a\u1001\u102f\u104f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1021\u1019\u103e\u1010\u103a\u1021\u1016\u103c\u1005\u103a \u101e\u102f\u1036\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/div>\n<div id=\"words_intro\"> \u1021\u101c\u102c\u1038\u1010\u1030\u104a \u1014\u1019\u1030\u1014\u102c\u1021\u1001\u103b\u102d\u102f\u1038\u1000\u102d\u102f \u101c\u1030\u1026\u1038\u101b\u1031\u1021\u1001\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1021\u1016\u103c\u1005\u103a \u101e\u102f\u1036\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u101c\u1030\u1026\u1038\u101b\u1031\u1021\u1001\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u1005\u103d\u102c \u101b\u103e\u102d\u1015\u103c\u102e\u1038\u104a \u1021\u1015\u102b\u1021\u101d\u1004\u103a\u104a<\/div>\n<div id=\"words_intro\"> <b>\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038 MLE \u1021\u1019\u103e\u1010\u103a<\/b> : x \/ n<\/div>\n<div id=\"words_intro\"> <b>\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038 Wilson \u1021\u1019\u103e\u1010\u103a<\/b> : (x + z <sup>2<\/sup> \/2) \/ (n + z <sup>2<\/sup> )<\/div>\n<div id=\"words_intro\"> <b>Jeffrey Point \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a<\/b> : (x + 0.5) \/ (n + 1)<\/div>\n<div id=\"words_intro\"> <b>Laplace \u1021\u1019\u103e\u1010\u103a\u104f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a<\/b> : (x + 1) \/ (n + 2)<\/div>\n<div id=\"words_intro\"> <b>x<\/b> \u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u101b\u103e\u102d &#8221;  hits &#8221;  \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 <b>n<\/b> \u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 <b>z<\/b> \u101e\u100a\u103a \u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1014\u103e\u1004\u1037\u103a\u1006\u1000\u103a\u1005\u1015\u103a\u1014\u1031\u101e\u100a\u1037\u103a z-score \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/div>\n<div id=\"words_intro\"> \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u101b\u103e\u102c\u101b\u1014\u103a\u104a \u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1019\u103e\u102f \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u104a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a \u1014\u103e\u1004\u1037\u103a \u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1019\u103e\u102f \u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1021\u1000\u103d\u1000\u103a\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1011\u100a\u1037\u103a\u1015\u102b\u104a \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a &#8220; \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1019\u100a\u103a&#8221;  \u1001\u101c\u102f\u1010\u103a\u1000\u102d\u102f \u1014\u103e\u102d\u1015\u103a\u1015\u102b\u104b<\/div>\n<div id=\"words\"> <label class=\"input_label_calc\" for=\"x\"><b>\u1021\u1031\u102c\u1004\u103a\u1019\u103c\u1004\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a (x)<\/b><\/label><input class=\"input_label_calc\" type=\"number\" id=\"x\" value=\"14\"> <label class=\"input_label_calc\" for=\"n\"><b>\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a (n)<\/b><\/label><input class=\"input_label_calc\" type=\"number\" id=\"n\" value=\"31\"> <label class=\"input_label_calc\" for=\"conf\"><b>\u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a (%)\u104a<\/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> \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a = <b><span id=\"best\">0.45695<\/span><\/b><\/p>\n<p> \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038 MLE \u1021\u1019\u103e\u1010\u103a = <span id=\"mle\">0.45161<\/span><\/p>\n<p> \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038 Wilson Point = <span id=\"wilson\">0.45695<\/span><\/p>\n<p> Jeffrey \u1021\u1019\u103e\u1010\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a = <span id=\"jeffrey\">0.45313<\/span><\/p>\n<p> \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031 Laplace \u1021\u1019\u103e\u1010\u103a = <span id=\"laplace\">0.45455<\/span><\/p>\n<\/div>\n<hr>\n<div id=\"words_intro\"> \u1024\u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a\u101e\u100a\u103a \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u1021\u1019\u103e\u1010\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1014\u103a \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u101a\u102f\u1010\u1039\u1010\u102d\u1017\u1031\u1012\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a-<\/div>\n<div id=\"words_intro\"> <b>x\/n \u2264 0.5<\/b> \u1016\u103c\u1005\u103a\u1015\u102b\u1000\u104a Wilson \u1021\u1019\u103e\u1010\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u104b<\/div>\n<div id=\"words_intro\"> \u1019\u101f\u102f\u1010\u103a\u101b\u1004\u103a <b>x\/n &lt; 0.9<\/b> \u1006\u102d\u102f\u101b\u1004\u103a MLE point estimation \u1000\u102d\u102f\u101e\u102f\u1036\u1038\u1015\u102b\u104b<\/div>\n<div id=\"words_intro\"> \u1019\u101f\u102f\u1010\u103a\u1015\u102b\u1000\u104a <b>x\/n &lt; 1.0<\/b> \u1006\u102d\u102f\u101c\u103b\u103e\u1004\u103a\u104a Jeffrey Point \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a Laplace Point Estimate \u104f\u1021\u101e\u1031\u1038\u1006\u102f\u1036\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u104b<\/div>\n<div id=\"words_intro\"> \u1019\u101f\u102f\u1010\u103a\u101b\u1004\u103a <b>x\/n = 1.0<\/b> \u1006\u102d\u102f\u101b\u1004\u103a Laplace point estimation \u1000\u102d\u102f\u101e\u102f\u1036\u1038\u1015\u102b\u104b<\/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 = wilson;\n} else if (val < 0.9) {\n  best = mle;\n} else if (val < 1) {\n  best = Math.min(laplace, jeffrey);\n} else {\n  best = laplace;\n}\n\n\/\/output results\ndocument.getElementById('best').innerHTML = best.toFixed(5);\ndocument.getElementById('mle').innerHTML = mle.toFixed(5);\ndocument.getElementById('wilson').innerHTML = wilson.toFixed(5);\ndocument.getElementById('jeffrey').innerHTML = jeffrey.toFixed(5);\ndocument.getElementById('laplace').innerHTML = laplace.toFixed(5);\n}\n\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u1021\u1019\u103e\u1010\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u101e\u100a\u103a \u101c\u1030\u1026\u1038\u101b\u1031\u1000\u1014\u1037\u103a\u101e\u1010\u103a\u1001\u103b\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u104f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f &#8220; \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a&#8221; \u1000\u102d\u102f \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1014\u1019\u1030\u1014\u102c\u1006\u102d\u102f\u101c\u102d\u102f\u1021\u102c\u1038 \u101c\u1030\u1026\u1038\u101b\u1031\u1010\u1005\u103a\u1001\u102f\u104f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1021\u1019\u103e\u1010\u103a\u1021\u1016\u103c\u1005\u103a \u101e\u102f\u1036\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u1021\u101c\u102c\u1038\u1010\u1030\u104a \u1014\u1019\u1030\u1014\u102c\u1021\u1001\u103b\u102d\u102f\u1038\u1000\u102d\u102f \u101c\u1030\u1026\u1038\u101b\u1031\u1021\u1001\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1021\u1016\u103c\u1005\u103a \u101e\u102f\u1036\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u101c\u1030\u1026\u1038\u101b\u1031\u1021\u1001\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a 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