{"id":456,"date":"2023-07-29T20:24:26","date_gmt":"2023-07-29T20:24:26","guid":{"rendered":"https:\/\/statorials.org\/ru\/dnorm-pnorm-rnorm-qnorm-%d0%b2-r\/"},"modified":"2023-07-29T20:24:26","modified_gmt":"2023-07-29T20:24:26","slug":"dnorm-pnorm-rnorm-qnorm-%d0%b2-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/ru\/dnorm-pnorm-rnorm-qnorm-%d0%b2-r\/","title":{"rendered":"\u0420\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e dnorm, pnorm, qnorm \u0438 rnorm \u0432 r"},"content":{"rendered":"

<\/p>\n

\n

\u041d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0447\u0430\u0441\u0442\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u044b\u043c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c \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 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432 R \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0439 dnorm<\/strong> , pnorm<\/strong> , rnorm<\/strong> \u0438 qnorm<\/strong> .<\/span><\/p>\n

\u0447\u0443\u0434\u043e\u0432\u0438\u0449\u043d\u044b\u0439<\/span><\/strong><\/h2>\n

\u0424\u0443\u043d\u043a\u0446\u0438\u044f dnorm<\/strong> \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) \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441 \u0443\u0447\u0435\u0442\u043e\u043c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b x<\/em> , \u0441\u0440\u0435\u0434\u043d\u0435\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0441\u043e\u0432\u043e\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0438 \u03bc<\/em> \u0438 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0433\u043e \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u044f \u0441\u043e\u0432\u043e\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0438 \u03c3<\/em> . \u0421\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f dnorm \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439:<\/span><\/p>\n

dnorm(x, \u0441\u0440\u0435\u0434\u043d\u0435\u0435, \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435)<\/span><\/strong><\/p>\n

\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\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 dnorm<\/strong> \u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0438:<\/span><\/p>\n

 #find the value of the standard normal distribution pdf at x=0<\/span>\ndnorm(x=0, mean=0, sd=1)\n#[1]0.3989423\n\n#by default, R uses mean=0 and sd=1<\/span>\ndnorm(x=0)\n#[1]0.3989423\n\n#find the value of the normal distribution pdf at x=10 with mean=20 and sd=5\ndnorm(x=10, mean=20, sd=5)<\/span>\n#[1]0.01079819<\/span><\/span>\n<\/strong><\/pre>\n
 \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, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435, \u0432\u044b \u0447\u0430\u0441\u0442\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0435 pnorm<\/strong> \u0432\u043c\u0435\u0441\u0442\u043e dnorm<\/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 dnorm<\/strong> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043e\u0437\u0434\u0430\u043d\u0438\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \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
 #Create a sequence of 100 equally spaced numbers between -4 and 4<\/span>\nx <- seq(-4, 4, length=100)\n\n#create a vector of values that shows the height of the probability distribution<\/span>\n#for each value in x<\/span>\ny <- dnorm(x)\n\n#plot x and y as a scatterplot with connected lines (type = \"l\") and add<\/span>\n#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
 \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
 \u043f\u043d\u043e\u0440\u043c<\/span><\/strong><\/h2>\n
 \u0424\u0443\u043d\u043a\u0446\u0438\u044f pnorm<\/strong> \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) \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441 \u0443\u0447\u0435\u0442\u043e\u043c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b q<\/em> , \u0441\u0440\u0435\u0434\u043d\u0435\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u043e\u043f\u0443\u043b\u044f\u0446\u0438\u0438 \u03bc<\/em> \u0438 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0433\u043e \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u044f \u0441\u043e\u0432\u043e\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0438 \u03c3<\/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
 pnorm(q, \u0441\u0440\u0435\u0434\u043d\u0435\u0435, \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435)<\/span><\/strong><\/p>\n
 \u041f\u0440\u043e\u0449\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, pnorm<\/strong> \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 x<\/em> \u0432 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u043c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0438. \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 q<\/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 low.tail = FALSE.<\/strong><\/span><\/p>\n
 pnorm(q, \u0441\u0440\u0435\u0434\u043d\u0435\u0435, \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435, \u043d\u0438\u0436\u043d\u0438\u0439.\u0445\u0432\u043e\u0441\u0442 = \u041b\u041e\u0416\u042c)<\/span><\/strong><\/p>\n
 \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 pnorm.<\/span><\/p>\n
 \u041f\u0440\u0438\u043c\u0435\u0440 1:<\/strong> \u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e \u0440\u043e\u0441\u0442 \u043c\u0443\u0436\u0447\u0438\u043d \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u0448\u043a\u043e\u043b\u0435 \u043e\u0431\u044b\u0447\u043d\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043e \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c \u03bc<\/span> = 70 \u0434\u044e\u0439\u043c\u043e\u0432 \u0438<\/span><\/span><\/span><\/span><\/span> \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u043c \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435\u043c \u03c3 = 2 \u0434\u044e\u0439\u043c\u0430.<\/span><\/span><\/span><\/span><\/span><\/em> \u041a\u0430\u043a\u043e\u0439 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e \u043f\u0440\u043e\u0446\u0435\u043d\u0442 \u043c\u0443\u0436\u0447\u0438\u043d \u0432 \u044d\u0442\u043e\u0439 \u0448\u043a\u043e\u043b\u0435 \u0438\u043c\u0435\u0435\u0442 \u0440\u043e\u0441\u0442 \u0431\u043e\u043b\u0435\u0435 74 \u0434\u044e\u0439\u043c\u043e\u0432?<\/span><\/span><\/span><\/span><\/span><\/em><\/span><\/p>\n
 #find percentage of males that are taller than 74 inches in a population with<\/span>\n#mean = 70 and sd = 2<\/span>\npnorm(74, mean=70, sd=2, lower.tail=FALSE)\n\n# [1]0.02275013<\/span><\/span><\/strong><\/pre>\n
 \u0412 \u044d\u0442\u043e\u0439 \u0448\u043a\u043e\u043b\u0435 2275% \u043c\u0443\u0436\u0447\u0438\u043d \u0438\u043c\u0435\u044e\u0442 \u0440\u043e\u0441\u0442 \u0431\u043e\u043b\u0435\u0435 74 \u0434\u044e\u0439\u043c\u043e\u0432.<\/span><\/p>\n
 \u041f\u0440\u0438\u043c\u0435\u0440 2:<\/strong> \u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e \u0432\u0435\u0441 \u0432\u044b\u0434\u0440\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0433\u043e \u0432\u0438\u0434\u0430 \u043e\u0431\u044b\u0447\u043d\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043e \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c \u00b5<\/span> = 30 \u0444\u0443\u043d\u0442\u043e\u0432 \u0438<\/span><\/span><\/span><\/span><\/span> \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u043c \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435\u043c \u03c3 = 5 \u0444\u0443\u043d\u0442\u043e\u0432. \u041f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043a\u0430\u043a\u043e\u0439 \u043f\u0440\u043e\u0446\u0435\u043d\u0442 \u0432\u044b\u0434\u0440 \u044d\u0442\u043e\u0433\u043e \u0432\u0438\u0434\u0430 \u0432\u0435\u0441\u0438\u0442 \u043c\u0435\u043d\u0435\u0435 22 \u0444\u0443\u043d\u0442\u043e\u0432?<\/span><\/span><\/span><\/span><\/span><\/em><\/span><\/p>\n
 #find percentage of otters that weight less than 22 lbs in a population with<\/span>\n#mean = 30 and sd = 5<\/span>\npnorm(22, mean=30, sd=5)\n\n# [1]0.05479929<\/span><\/span><\/strong><\/pre>\n
 \u041e\u043a\u043e\u043b\u043e 5,4799% \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u0435\u043b\u0435\u0439 \u044d\u0442\u043e\u0433\u043e \u0432\u0438\u0434\u0430 \u0432\u044b\u0434\u0440 \u0432\u0435\u0441\u044f\u0442 \u043c\u0435\u043d\u0435\u0435 22 \u0444\u0443\u043d\u0442\u043e\u0432.<\/span><\/p>\n
 \u041f\u0440\u0438\u043c\u0435\u0440 3:<\/strong> \u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e \u0432\u044b\u0441\u043e\u0442\u0430 \u0440\u0430\u0441\u0442\u0435\u043d\u0438\u0439 \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u043c \u0440\u0435\u0433\u0438\u043e\u043d\u0435 \u043e\u0431\u044b\u0447\u043d\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043e \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c \u03bc<\/span> = 13 \u0434\u044e\u0439\u043c\u043e\u0432 \u0438<\/span><\/span><\/span><\/span><\/span> \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u043c \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435\u043c \u03c3 = 2 \u0434\u044e\u0439\u043c\u0430. \u041f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043a\u0430\u043a\u043e\u0439 \u043f\u0440\u043e\u0446\u0435\u043d\u0442 \u0440\u0430\u0441\u0442\u0435\u043d\u0438\u0439 \u0432 \u044d\u0442\u043e\u043c \u0440\u0435\u0433\u0438\u043e\u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u0432\u044b\u0441\u043e\u0442\u0443 \u043e\u0442 10 \u0434\u043e 14 \u0434\u044e\u0439\u043c\u043e\u0432?<\/span><\/span><\/span><\/span><\/span><\/em><\/span><\/p>\n
 #find percentage of plants that are less than 14 inches tall, then subtract the\n#percentage of plants that are less than 10 inches tall, based on a population\n#with mean = 13 and sd = 2<\/span>\npnorm(14, mean=13, sd=2) - pnorm(10, mean=13, sd=2)\n\n# [1]0.6246553<\/span><\/span><\/strong><\/pre>\n
 \u041e\u043a\u043e\u043b\u043e 62,4655% \u0440\u0430\u0441\u0442\u0435\u043d\u0438\u0439 \u0432 \u044d\u0442\u043e\u043c \u0440\u0435\u0433\u0438\u043e\u043d\u0435 \u0438\u043c\u0435\u044e\u0442 \u0432\u044b\u0441\u043e\u0442\u0443 \u043e\u0442 10 \u0434\u043e 14 \u0434\u044e\u0439\u043c\u043e\u0432.<\/span><\/p>\n
 \u043d\u043e\u0440\u043c\u0430<\/span><\/strong><\/h2>\n
 \u0424\u0443\u043d\u043a\u0446\u0438\u044f qnorm<\/strong> \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) \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441 \u0443\u0447\u0435\u0442\u043e\u043c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b p<\/em> , \u0441\u0440\u0435\u0434\u043d\u0435\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u043e\u043f\u0443\u043b\u044f\u0446\u0438\u0438 \u03bc<\/em> \u0438 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0433\u043e \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u044f \u0441\u043e\u0432\u043e\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0438 \u03c3<\/em> . \u0421\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f qnorm \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439:<\/span><\/p>\n
 qnorm (p, \u0441\u0440\u0435\u0434\u043d\u0435\u0435, \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435)<\/span><\/strong><\/p>\n
 \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 qnorm<\/strong> , \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u043a\u0430\u043a\u043e\u0432 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c Z p-<\/sup> \u0433\u043e \u043a\u0432\u0430\u043d\u0442\u0438\u043b\u044f \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f.<\/span><\/p>\n
 \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\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 qnorm<\/strong> \u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0438:<\/span><\/p>\n
 #find the Z-score of the 99th quantile of the standard normal distribution<\/span> \nqnorm(.99, mean=0, sd=1)\n#[1]2.326348\n\n#by default, R uses mean=0 and sd=1\nqnorm(.99)<\/span>\n#[1]2.326348\n\n#find the Z-score of the 95th quantile of the standard normal distribution<\/span>\nqnorm(.95)\n#[1]1.644854\n\n#find the Z-score of the 10th quantile of the standard normal distribution<\/span>\nqnorm(.10)\n#[1]-1.281552<\/span>\n<\/span><\/strong><\/pre>\n
 \u043d\u043e\u0440\u043c\u0430<\/span><\/strong><\/h2>\n
 \u0424\u0443\u043d\u043a\u0446\u0438\u044f rnorm<\/strong> \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u0435\u0442 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0445 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0445 \u0432\u0435\u043b\u0438\u0447\u0438\u043d \u0441 \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u0439 \u0434\u043b\u0438\u043d\u043e\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 n<\/em> , \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u043b\u044c\u043d\u043e\u0439 \u0441\u043e\u0432\u043e\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0438 \u03bc<\/em> \u0438 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u043c \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435\u043c \u0433\u0435\u043d\u0435\u0440\u0430\u043b\u044c\u043d\u043e\u0439 \u0441\u043e\u0432\u043e\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0438 \u03c3<\/em> . \u0421\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f rnorm \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439:<\/span><\/p>\n
 rnorm(n, \u0441\u0440\u0435\u0434\u043d\u0435\u0435, \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435)<\/span><\/strong><\/p>\n
 \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\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 rnorm<\/strong> \u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0438:<\/span><\/p>\n
 #generate a vector of 5 normally distributed random variables with mean=10 and sd=2<\/span>\nfive <- rnorm(5, mean = 10, sd = 2)\nfive\n# [1] 10.658117 8.613495 10.561760 11.123492 10.802768\n\n#generate a vector of 1000 normally distributed random variables with mean=50 and sd=5\n<\/span>narrowDistribution <- rnorm(1000, mean = 50, sd = 15)\n\n<\/span>#generate a vector of 1000 normally distributed random variables with mean=50 and sd=25<\/span>\nwideDistribution <- rnorm(1000, mean = 50, sd = 25)\n\n<\/span>#generate two histograms to view these two distributions side by side, specify\n#50 bars in histogram and x-axis limits of -50 to 150\npar(mfrow=c(1, 2)) #one row, two columns<\/span>\nhist(narrowDistribution, breaks=50, xlim=c(-50, 150))<\/span>\nhist(wideDistribution, breaks=50, xlim=c(-50, 150))<\/span>\n<\/span><\/span><\/span><\/strong><\/pre>\n
 \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
 \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 \u043d\u0430\u043c\u043d\u043e\u0433\u043e \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\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435 \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\u043e 25 \u043f\u043e \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0441 \u0432\u0441\u0435\u0433\u043e \u043b\u0438\u0448\u044c 15 \u0432 \u0443\u0437\u043a\u043e\u043c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0438. \u0422\u0430\u043a\u0436\u0435 \u043e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u043e\u0431\u0435 \u0433\u0438\u0441\u0442\u043e\u0433\u0440\u0430\u043c\u043c\u044b \u0441\u043e\u0441\u0440\u0435\u0434\u043e\u0442\u043e\u0447\u0435\u043d\u044b \u0432\u043e\u043a\u0440\u0443\u0433 \u0441\u0440\u0435\u0434\u043d\u0435\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f 50.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
\u041d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0447\u0430\u0441\u0442\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u044b\u043c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c \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 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432 R \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0439 dnorm , pnorm , rnorm \u0438 qnorm . \u0447\u0443\u0434\u043e\u0432\u0438\u0449\u043d\u044b\u0439 \u0424\u0443\u043d\u043a\u0446\u0438\u044f dnorm \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) \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441 \u0443\u0447\u0435\u0442\u043e\u043c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b x , \u0441\u0440\u0435\u0434\u043d\u0435\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0441\u043e\u0432\u043e\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0438 \u03bc \u0438 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0433\u043e \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u044f […]<\/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-456","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"\n\u0420\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e dnorm, pnorm, qnorm \u0438 rnorm \u0432 R \u2014 \u0421\u0442\u0430\u0442\u043e\u0440\u0438\u0430\u043b\u044b<\/title>\n<meta name=\"description\" content=\"\u041f\u0440\u043e\u0441\u0442\u043e\u0435 \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c dnorm, pnorm, rnorm \u0438 qnorm \u0432 R.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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