{"id":494,"date":"2023-07-29T17:37:17","date_gmt":"2023-07-29T17:37:17","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%9c%a8-r-dt-qt-pt-rt-%e4%b8%ad%e5%a4%84%e7%90%86%e5%ad%a6%e7%94%9f-t-%e5%88%86%e5%b8%83\/"},"modified":"2023-07-29T17:37:17","modified_gmt":"2023-07-29T17:37:17","slug":"%e5%9c%a8-r-dt-qt-pt-rt-%e4%b8%ad%e5%a4%84%e7%90%86%e5%ad%a6%e7%94%9f-t-%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%9c%a8-r-dt-qt-pt-rt-%e4%b8%ad%e5%a4%84%e7%90%86%e5%ad%a6%e7%94%9f-t-%e5%88%86%e5%b8%83\/","title":{"rendered":"R \u4e2d dt\u3001qt\u3001pt \u548c rt \u6307\u5357"},"content":{"rendered":"<p><span style=\"color: #000000;\"><strong>Student t \u5206\u5e03<\/strong>\u662f\u7edf\u8ba1\u5b66\u4e2d\u6700\u5e38\u7528\u7684\u5206\u5e03\u4e4b\u4e00\u3002\u672c\u6559\u7a0b\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528<strong>dt()<\/strong> \u3001 <strong>qt()<\/strong> \u3001 <strong>pt()<\/strong>\u548c<strong>rt()<\/strong>\u51fd\u6570\u5728 R \u4e2d\u5904\u7406 Student t \u5206\u5e03\u3002<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">dt<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u51fd\u6570<b>dt<\/b>\u8fd4\u56de\u7ed9\u5b9a\u67d0\u4e2a\u968f\u673a\u53d8\u91cf<em>x<\/em>\u548c\u81ea\u7531\u5ea6<em>df<\/em>\u7684\u5b66\u751f t \u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570 (pdf) \u503c\u3002\u4f7f\u7528dt\u7684\u8bed\u6cd5\u5982\u4e0b\uff1a<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">dt(x, df)<\/span><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u6f14\u793a\u4e86<b>dt<\/b>\u7684\u4e00\u4e9b\u5b9e\u9645\u64cd\u4f5c\u793a\u4f8b\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find the value of the Student t distribution pdf at x = 0 with 20 degrees of freedom<\/span>\ndt(x = 0, df = 20)\n\n#[1] 0.3939886\n<span style=\"color: #008080;\">\n#by default, R assumes the first argument is <em>x<\/em> and the second argument is <em>df<\/em><\/span>\ndt(0, 20)\n\n#[1] 0.3939886\n<span style=\"color: #008080;\">#find the value of the Student t distribution pdf at x = 1 with 30 degrees of freedom\n<span style=\"color: #000000;\">dt(1, 30)\n<\/span>\n<span style=\"color: #000000;\">#[1] 0.2379933\n<\/span><\/span><\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u901a\u5e38\uff0c\u5f53\u5c1d\u8bd5\u4f7f\u7528\u5b66\u751f t \u5206\u5e03\u89e3\u51b3\u6709\u5173\u6982\u7387\u7684\u95ee\u9898\u65f6\uff0c\u60a8\u901a\u5e38\u4f1a\u4f7f\u7528<b>pt<\/b>\u800c\u4e0d\u662f<strong>dt<\/strong> \u3002\u7136\u800c\uff0c <strong>dt<\/strong>\u7684\u4e00\u4e2a\u6709\u7528\u5e94\u7528\u662f\u5728 R \u4e2d\u521b\u5efa\u5b66\u751f t \u5206\u5e03\u56fe\u3002\u4ee5\u4e0b\u4ee3\u7801\u8bf4\u660e\u4e86\u5982\u4f55\u6267\u884c\u6b64\u64cd\u4f5c\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#Create a sequence of 100 equally spaced numbers between -4 and 4<\/span>\nx &lt;- seq(-4, 4, length=100)\n\n<span style=\"color: #008080;\">#create a vector of values that shows the height of the probability distribution<\/span>\n<span style=\"color: #008080;\">#for each value in x, using 20 degrees of freedom<\/span>\ny &lt;- dt(x = x, df = 20)\n\n<span style=\"color: #008080;\">#plot x and y as a scatterplot with connected lines (type = \"l\") and add<\/span>\n<span style=\"color: #008080;\">#an x-axis with custom labels<\/span>\nplot(x,y, type = \"l\", lwd = 2, axes = FALSE, xlab = \"\", ylab = \"\")\naxis(1, at = -3:3, labels = c(\"-3s\", \"-2s\", \"-1s\", \"mean\", \"1s\", \"2s\", \"3s\"))<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u8fd9\u4f1a\u751f\u6210\u4ee5\u4e0b\u56fe\uff1a<\/span><\/p>\n<h2><strong><span style=\"color: #000000;\">\u70b9<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\"><b>pt<\/b>\u51fd\u6570\u8fd4\u56de\u7ed9\u5b9a\u67d0\u4e2a\u968f\u673a\u53d8\u91cf<em>x<\/em>\u548c\u81ea\u7531\u5ea6<em>df<\/em>\u7684\u5b66\u751f t \u5206\u5e03\u7684\u7d2f\u79ef\u5bc6\u5ea6\u51fd\u6570 (cdf) \u7684\u503c\u3002\u4f7f\u7528 pnorm \u7684\u8bed\u6cd5\u5982\u4e0b\uff1a<\/span><\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #000000;\">\u70b9\uff08x\uff0cdf\uff09<\/span><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u7b80\u5355\u6765\u8bf4\uff0c <b>pt<\/b>\u8fd4\u56de\u5b66\u751f t \u5206\u5e03\u4e2d\u7ed9\u5b9a<em>x<\/em>\u503c\u5de6\u4fa7\u7684\u9762\u79ef\u3002\u5982\u679c\u60a8\u5bf9\u7ed9\u5b9a<em>x<\/em>\u503c\u53f3\u4fa7\u7684\u533a\u57df\u611f\u5174\u8da3\uff0c\u60a8\u53ef\u4ee5\u7b80\u5355\u5730\u6dfb\u52a0\u53c2\u6570<strong>lower.tail = FALSE<\/strong><\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">pt(x, df, lower.tail = FALSE)<\/span><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u8bf4\u660e\u4e86\u5982\u4f55\u4f7f\u7528 pt \u89e3\u51b3\u4e00\u4e9b\u6982\u7387\u95ee\u9898\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u793a\u4f8b 1\uff1a<\/strong><em>\u67e5\u627e\u503c\u4e3a -0.785\u3001\u81ea\u7531\u5ea6\u4e3a 14 \u7684 t \u7edf\u8ba1\u91cf<strong>\u5de6\u4fa7<\/strong>\u7684\u9762\u79ef\u3002<\/em><\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\">pt(-0.785, 14)\n\n#[1] 0.2227675\n<\/span><\/span><\/strong><\/pre>\n<p><span style=\"color: #000000;\"><strong>\u793a\u4f8b 2\uff1a<\/strong><em>\u67e5\u627e\u503c\u4e3a -0.785\u3001\u81ea\u7531\u5ea6\u4e3a 14 \u7684 t \u7edf\u8ba1\u91cf<strong>\u53f3\u4fa7<\/strong>\u7684\u9762\u79ef\u3002<\/em><\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008080;\">#the following approaches produce equivalent results\n\n#1 - area to the left<\/span>\n1 - pt(-0.785, 14)\n\n#[1] 0.7772325\n\n<span style=\"color: #008080;\">#area to the right<\/span>\npt(-0.785, 14, lower.tail = FALSE)\n\n#[1] 0.7772325 \n<\/span><\/span><\/span><\/strong><\/pre>\n<p><span style=\"color: #000000;\"><strong>\u793a\u4f8b 3\uff1a<\/strong><em>\u67e5\u627e\u4f4d\u4e8e -0.785 \u5de6\u4fa7\u6216 0.785 \u53f3\u4fa7\u3001\u5177\u6709 14 \u4e2a\u81ea\u7531\u5ea6\u7684 Student t \u5206\u5e03\u4e2d\u7684\u603b\u9762\u79ef\u3002<\/em><\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>pt <span style=\"color: #008080;\"><span style=\"color: #000000;\">(-0.785, 14)<\/span><\/span> + pt <span style=\"color: #008080;\"><span style=\"color: #000000;\">(0.785, 14, lower.tail = FALSE)<\/span><\/span>\n\n#[1] 0.4455351<\/strong><\/pre>\n<h2> <strong><span style=\"color: #000000;\">qt<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u51fd\u6570<b>qt<\/b>\u8fd4\u56de\u7ed9\u5b9a\u67d0\u4e2a\u968f\u673a\u53d8\u91cf<em>x<\/em>\u548c\u81ea\u7531\u5ea6<em>df \u7684\u5b66\u751f t \u5206\u5e03\u7684\u9006\u7d2f\u79ef\u5bc6\u5ea6\u51fd\u6570 (cdf) \u7684\u503c\u3002<\/em>\u4f7f\u7528qt\u7684\u8bed\u6cd5\u5982\u4e0b\uff1a<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">qt(x, df)<\/span><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u7b80\u5355\u6765\u8bf4\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528<strong>qt<\/strong>\u627e\u51fa\u5b66\u751f t \u5206\u5e03\u7684<sup>\u7b2c p \u5206<\/sup>\u4f4d\u6570\u7684 t \u5206\u6570\u662f\u591a\u5c11\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u6f14\u793a\u4e86<b>qt<\/b>\u7684\u4e00\u4e9b\u5b9e\u9645\u64cd\u4f5c\u793a\u4f8b\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find the t-score of the 99th quantile of the Student t distribution with df = 20\n<\/span>qt(.99, df = 20)\n\n#[1][1]2.527977<span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008080;\">\n\n#find the t-score of the 95th quantile of the Student t distribution with df = 20<\/span>\nqt(.95, df = 20)\n\n#[1]1.724718\n\n<span style=\"color: #008080;\">#find the t-score of the 90th quantile of the Student t distribution with df = 20<\/span>\nqt(.9, df = 20)\n\n#[1]1.325341<\/span>\n<\/span><\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u8bf7\u6ce8\u610f\uff0c <strong>qt<\/strong>\u627e\u5230\u7684\u4e34\u754c\u503c\u5c06\u5bf9\u5e94\u4e8e t \u5206\u5e03\u8868\u4e2d\u627e\u5230\u7684\u4e34\u754c\u503c\u4ee5\u53ca\u9006 t \u5206\u5e03\u8ba1\u7b97\u5668\u53ef\u4ee5\u627e\u5230\u7684\u4e34\u754c\u503c\u3002<\/span><\/p>\n<h2><strong><span style=\"color: #000000;\">\u5ba4\u6e29<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u51fd\u6570<b>rt<\/b>\u751f\u6210\u4e00\u4e2a\u968f\u673a\u53d8\u91cf\u5411\u91cf\uff0c\u5728\u7ed9\u5b9a\u5411\u91cf\u957f\u5ea6<em>n<\/em>\u548c\u81ea\u7531\u5ea6<em>df<\/em>\u7684\u60c5\u51b5\u4e0b\uff0c\u8be5\u5411\u91cf\u9075\u5faa\u5b66\u751f t \u5206\u5e03\u3002\u4f7f\u7528rt\u7684\u8bed\u6cd5\u5982\u4e0b\uff1a<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">rt(n, df)<\/span><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u6f14\u793a\u4e86<b>rt<\/b>\u7684\u4e00\u4e9b\u5b9e\u9645\u64cd\u4f5c\u793a\u4f8b\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#generate a vector of 5 random variables that follows a Student t distribution\n#with df = 20<\/span>\nrt(n = 5, df = 20)\n\n#[1] -1.7422445 0.9560782 0.6635823 1.2122289 -0.7052825\n\n<span style=\"color: #008080;\">#generate a vector of 1000 random variables that follows a Student t distribution\n#with df = 40\n<span style=\"color: #000000;\">narrowDistribution &lt;- rt(1000, 40)\n\n<span style=\"color: #008080;\">#generate a vector of 1000 random variables that follows a Student t distribution\n#with df = 5\n<\/span>wideDistribution &lt;- rt(1000, 5)\n\n<span style=\"color: #008080;\">#generate two histograms to view these two distributions side by side, and specify\n#50 bars in histogram,<\/span>\npar(mfrow=c(1, 2)) #one row, two columns\nhist(narrowDistribution, breaks=50, xlim = c(-6, 4)) \nhist(wideDistribution, breaks=50, xlim = c(-6, 4))\n<\/span><\/span><\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u8fd9\u4f1a\u751f\u6210\u4ee5\u4e0b\u76f4\u65b9\u56fe\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8bf7\u6ce8\u610f\u5bbd\u5206\u5e03\u6bd4\u7a84\u5206\u5e03\u66f4\u5bbd\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u6307\u5b9a\u5bbd\u5206\u5e03\u4e2d\u7684\u81ea\u7531\u5ea6\u4e3a 5\uff0c\u800c\u7a84\u5206\u5e03\u4e2d\u7684\u81ea\u7531\u5ea6\u4e3a 40\u3002\u81ea\u7531\u5ea6\u8d8a\u5c11\uff0cStudent t \u5206\u5e03\u5c31\u8d8a\u5bbd\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u8fdb\u4e00\u6b65\u9605\u8bfb\uff1a<br \/> <a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\">R \u4e2d dnorm\u3001pnorm\u3001qnorm \u548c rnorm \u6307\u5357<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\">R \u4e2d\u7684 dbinom\u3001pbinom\u3001qbinom \u548c rbinom \u6307\u5357<\/a><br \/><\/strong><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Student t \u5206\u5e03\u662f\u7edf\u8ba1\u5b66\u4e2d\u6700\u5e38\u7528\u7684\u5206\u5e03\u4e4b\u4e00\u3002\u672c\u6559\u7a0b\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528dt() \u3001 qt() \u3001 pt()\u548cr [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-494","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R \u4e2d dt\u3001qt\u3001pt \u548c rt \u6307\u5357 - Statorials<\/title>\n<meta name=\"description\" content=\"\u672c\u6559\u7a0b\u7b80\u5355\u8bf4\u660e\u4e86\u5982\u4f55\u4f7f\u7528 dt()\u3001qt()\u3001pt() \u548c rt() \u51fd\u6570\u5728 R \u4e2d\u5904\u7406 Student t \u5206\u5e03\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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