{"id":490,"date":"2023-07-29T17:37:17","date_gmt":"2023-07-29T17:37:17","guid":{"rendered":"https:\/\/statorials.org\/ru\/%d1%80%d0%b0%d0%b1%d0%be%d1%82%d0%b0-%d1%81-%d1%80%d0%b0%d1%81%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d0%b5%d0%bc-%d1%81%d1%82%d1%83%d0%b4%d0%b5%d0%bd%d1%82%d0%be%d0%b2-%d0%b2-r-dt-qt-p\/"},"modified":"2023-07-29T17:37:17","modified_gmt":"2023-07-29T17:37:17","slug":"%d1%80%d0%b0%d0%b1%d0%be%d1%82%d0%b0-%d1%81-%d1%80%d0%b0%d1%81%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d0%b5%d0%bc-%d1%81%d1%82%d1%83%d0%b4%d0%b5%d0%bd%d1%82%d0%be%d0%b2-%d0%b2-r-dt-qt-p","status":"publish","type":"post","link":"https:\/\/statorials.org\/ru\/%d1%80%d0%b0%d0%b1%d0%be%d1%82%d0%b0-%d1%81-%d1%80%d0%b0%d1%81%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d0%b5%d0%bc-%d1%81%d1%82%d1%83%d0%b4%d0%b5%d0%bd%d1%82%d0%be%d0%b2-%d0%b2-r-dt-qt-p\/","title":{"rendered":"\u0420\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e dt, qt, pt \u0438 rt \u0432 r"},"content":{"rendered":"<p><span style=\"color: #000000;\"><strong>\u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430<\/strong> \u2014 \u043e\u0434\u043d\u043e \u0438\u0437 \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0447\u0430\u0441\u0442\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u044b\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439 \u0432 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0435. \u0412 \u044d\u0442\u043e\u043c \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442\u0441\u044f, \u043a\u0430\u043a \u0440\u0430\u0431\u043e\u0442\u0430\u0442\u044c \u0441 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c t \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430 \u0432 R \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0439 <strong>dt()<\/strong> , <strong>qt()<\/strong> , <strong>pt()<\/strong> \u0438 <strong>rt()<\/strong> .<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">\u0434\u0442<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">\u0424\u0443\u043d\u043a\u0446\u0438\u044f <b>dt<\/b> \u0432\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 (pdf) \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430 t \u0441 \u0443\u0447\u0435\u0442\u043e\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b <em>x<\/em> \u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0441\u0432\u043e\u0431\u043e\u0434\u044b <em>df<\/em> . \u0421\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f dt \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439:<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">\u0434\u0442(\u0445, \u0434\u0444)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u0421\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043a\u043e\u0434 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u0442 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b <b>dt<\/b> \u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0438:<\/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;\">\u041e\u0431\u044b\u0447\u043d\u043e, \u043f\u044b\u0442\u0430\u044f\u0441\u044c \u0440\u0435\u0448\u0438\u0442\u044c \u0432\u043e\u043f\u0440\u043e\u0441\u044b \u043e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430, \u0432\u044b \u0447\u0430\u0441\u0442\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0435 <b>pt<\/b> \u0432\u043c\u0435\u0441\u0442\u043e <strong>dt<\/strong> . \u041e\u0434\u043d\u0430\u043a\u043e \u043f\u043e\u043b\u0435\u0437\u043d\u044b\u043c \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435\u043c <strong>dt<\/strong> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043e\u0437\u0434\u0430\u043d\u0438\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430 \u0432 R. \u0421\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043a\u043e\u0434 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u043a\u0430\u043a \u044d\u0442\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c:<\/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;\">\u042d\u0442\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0433\u0440\u0430\u0444\u0438\u043a:<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">\u043f\u0442<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">\u0424\u0443\u043d\u043a\u0446\u0438\u044f <b>pt<\/b> \u0432\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043a\u0443\u043c\u0443\u043b\u044f\u0442\u0438\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 (cdf) \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430 t \u0441 \u0443\u0447\u0435\u0442\u043e\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b <em>x<\/em> \u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0441\u0432\u043e\u0431\u043e\u0434\u044b <em>df<\/em> . \u0421\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f pnorm \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439:<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">\u043f\u0442(\u0445, \u0434\u0444)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u041f\u0440\u043e\u0449\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, <b>pt<\/b> \u0432\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0441\u043b\u0435\u0432\u0430 \u043e\u0442 \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <em>x<\/em> \u0432 t-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0438 \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430. \u0415\u0441\u043b\u0438 \u0432\u0430\u0441 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u0443\u0435\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0441\u043f\u0440\u0430\u0432\u0430 \u043e\u0442 \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <em>x<\/em> , \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u0434\u043e\u0431\u0430\u0432\u0438\u0442\u044c \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442 <strong>low.tail = FALSE.<\/strong><\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">pt(x, df, \u043d\u0438\u0436\u043d\u0438\u0439.\u0445\u0432\u043e\u0441\u0442 = \u041b\u041e\u0416\u042c)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u0421\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0438\u043b\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u0443\u044e\u0442, \u043a\u0430\u043a \u0440\u0435\u0448\u0430\u0442\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u044b\u0435 \u0432\u043e\u043f\u0440\u043e\u0441\u044b \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e pt.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u041f\u0440\u0438\u043c\u0435\u0440 1.<\/strong> <em>\u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u044c <strong>\u0441\u043b\u0435\u0432\u0430<\/strong> \u043e\u0442 t-\u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0438 \u0441\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c -0,785 \u0438 14 \u0441\u0442\u0435\u043f\u0435\u043d\u044f\u043c\u0438 \u0441\u0432\u043e\u0431\u043e\u0434\u044b.<\/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>\u041f\u0440\u0438\u043c\u0435\u0440 2:<\/strong> <em>\u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u044c <strong>\u0441\u043f\u0440\u0430\u0432\u0430<\/strong> \u043e\u0442 t-\u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0438 \u0441\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c -0,785 \u0438 14 \u0441\u0442\u0435\u043f\u0435\u043d\u044f\u043c\u0438 \u0441\u0432\u043e\u0431\u043e\u0434\u044b.<\/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>\u041f\u0440\u0438\u043c\u0435\u0440 3:<\/strong> <em>\u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043e\u0431\u0449\u0443\u044e \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0432 t-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0438 \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430 \u0441 14 \u0441\u0442\u0435\u043f\u0435\u043d\u044f\u043c\u0438 \u0441\u0432\u043e\u0431\u043e\u0434\u044b, \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u043d\u044b\u043c\u0438 \u0441\u043b\u0435\u0432\u0430 \u043e\u0442 -0,785 \u0438\u043b\u0438 \u0441\u043f\u0440\u0430\u0432\u0430 \u043e\u0442 0,785.<\/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;\">\u0424\u0443\u043d\u043a\u0446\u0438\u044f <b>qt<\/b> \u0432\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0439 \u043a\u0443\u043c\u0443\u043b\u044f\u0442\u0438\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 (cdf) \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430 t \u043f\u0440\u0438 \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0435 <em>x<\/em> \u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u044f\u0445 \u0441\u0432\u043e\u0431\u043e\u0434\u044b <em>df.<\/em> \u0421\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f qt \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439:<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">qt(\u0445, \u0434\u0444)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u041f\u0440\u043e\u0449\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c <strong>qt<\/strong> , \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u043a\u0430\u043a\u043e\u0432 t-\u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c <sup>p-\u0433\u043e<\/sup> \u043a\u0432\u0430\u043d\u0442\u0438\u043b\u044f t-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0421\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043a\u043e\u0434 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u0442 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b <b>qt<\/b> \u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0438:<\/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;\">\u041e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0435 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e <strong>qt,<\/strong> \u0431\u0443\u0434\u0443\u0442 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u043e\u0432\u0430\u0442\u044c \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c, \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u043c \u0432 \u0442\u0430\u0431\u043b\u0438\u0446\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f t, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043a\u0430\u043b\u044c\u043a\u0443\u043b\u044f\u0442\u043e\u0440\u0430 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f t.<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">\u0440\u0442<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">\u0424\u0443\u043d\u043a\u0446\u0438\u044f <b>rt<\/b> \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u0435\u0442 \u0432\u0435\u043a\u0442\u043e\u0440 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0445 \u0432\u0435\u043b\u0438\u0447\u0438\u043d, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430 t \u043f\u0440\u0438 \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u0439 \u0434\u043b\u0438\u043d\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 <em>n<\/em> \u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u044f\u0445 \u0441\u0432\u043e\u0431\u043e\u0434\u044b <em>df<\/em> . \u0421\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f rt \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439:<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">\u0440\u0442(\u043f, \u0434\u0444)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u0421\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043a\u043e\u0434 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u0442 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b <b>rt<\/b> \u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0438:<\/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;\">\u042d\u0442\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0433\u0438\u0441\u0442\u043e\u0433\u0440\u0430\u043c\u043c\u044b:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u041e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u0448\u0438\u0440\u043e\u043a\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0448\u0438\u0440\u0435 \u0443\u0437\u043a\u043e\u0433\u043e. \u0414\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u044b \u0443\u043a\u0430\u0437\u0430\u043b\u0438, \u0447\u0442\u043e \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0441\u0432\u043e\u0431\u043e\u0434\u044b \u0432 \u0448\u0438\u0440\u043e\u043a\u043e\u043c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0438 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u043b\u0438 5 \u043f\u043e \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0441 40 \u0432 \u0443\u0437\u043a\u043e\u043c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0438. \u0427\u0435\u043c \u043c\u0435\u043d\u044c\u0448\u0435 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0441\u0432\u043e\u0431\u043e\u0434\u044b, \u0442\u0435\u043c \u0448\u0438\u0440\u0435 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0414\u0430\u043b\u044c\u043d\u0435\u0439\u0448\u0435\u0435 \u0447\u0442\u0435\u043d\u0438\u0435:<br \/> \u0420\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e dnorm, pnorm, qnorm \u0438 rnorm \u0432 R<br \/> \u0420\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e dbinom, pbinom, qbinom \u0438 rbinom \u0432 R<br \/><\/strong><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430 \u2014 \u043e\u0434\u043d\u043e \u0438\u0437 \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0447\u0430\u0441\u0442\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u044b\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439 \u0432 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0435. \u0412 \u044d\u0442\u043e\u043c \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442\u0441\u044f, \u043a\u0430\u043a \u0440\u0430\u0431\u043e\u0442\u0430\u0442\u044c \u0441 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c t \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430 \u0432 R \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0439 dt() , qt() , pt() \u0438 rt() . \u0434\u0442 \u0424\u0443\u043d\u043a\u0446\u0438\u044f dt \u0432\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 (pdf) \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430 t \u0441 \u0443\u0447\u0435\u0442\u043e\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b x \u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0441\u0432\u043e\u0431\u043e\u0434\u044b [&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-490","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>\u0420\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e dt, qt, pt \u0438 rt \u0432 R \u2014 \u0421\u0442\u0430\u0442\u043e\u0440\u0438\u0430\u043b\u044b<\/title>\n<meta name=\"description\" content=\"\u0412 \u044d\u0442\u043e\u043c \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043e \u043f\u0440\u043e\u0441\u0442\u043e\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a 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