{"id":491,"date":"2023-07-29T17:37:17","date_gmt":"2023-07-29T17:37:17","guid":{"rendered":"https:\/\/statorials.org\/ja\/r-dt-qt-pt-rt-%e3%81%a6%e3%82%99%e5%ad%a6%e7%94%9f%e3%81%ae-t-%e5%88%86%e5%b8%83%e3%82%92%e6%93%8d%e4%bd%9c%e3%81%99%e3%82%8b\/"},"modified":"2023-07-29T17:37:17","modified_gmt":"2023-07-29T17:37:17","slug":"r-dt-qt-pt-rt-%e3%81%a6%e3%82%99%e5%ad%a6%e7%94%9f%e3%81%ae-t-%e5%88%86%e5%b8%83%e3%82%92%e6%93%8d%e4%bd%9c%e3%81%99%e3%82%8b","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/r-dt-qt-pt-rt-%e3%81%a6%e3%82%99%e5%ad%a6%e7%94%9f%e3%81%ae-t-%e5%88%86%e5%b8%83%e3%82%92%e6%93%8d%e4%bd%9c%e3%81%99%e3%82%8b\/","title":{"rendered":"R \u306e dt\u3001qt\u3001pt\u3001rt \u306e\u30ac\u30a4\u30c9"},"content":{"rendered":"

\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306f\u3001<\/strong>\u7d71\u8a08\u3067\u6700\u3082\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u5206\u5e03\u306e 1 \u3064\u3067\u3059\u3002\u3053\u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u3067\u306f\u3001 dt()<\/strong> \u3001 qt()<\/strong> \u3001 pt()<\/strong>\u304a\u3088\u3073rt()<\/strong>\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001R \u3067 Student t \u5206\u5e03\u3092\u64cd\u4f5c\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/span><\/p>\n

dt<\/span><\/strong><\/h2>\n

\u95a2\u6570dt \u306f<\/b>\u3001\u7279\u5b9a\u306e\u78ba\u7387\u5909\u6570x<\/em>\u3068\u81ea\u7531\u5ea6df<\/em>\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u306e\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8 t \u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570 (pdf) \u306e\u5024\u3092\u8fd4\u3057\u307e\u3059\u3002 dt \u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u306e\u69cb\u6587\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/span><\/p>\n

dt(x, df)<\/span><\/strong><\/p>\n

\u6b21\u306e\u30b3\u30fc\u30c9\u306f\u3001 dt<\/b>\u306e\u52d5\u4f5c\u4f8b\u3092\u3044\u304f\u3064\u304b\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n

 #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\n#by default, R assumes the first argument is x<\/em> and the second argument is df<\/em><\/span>\ndt(0, 20)\n\n#[1] 0.3939886\n#find the value of the Student t distribution pdf at x = 1 with 30 degrees of freedom\ndt(1, 30)\n<\/span>\n#[1] 0.2379933\n<\/span><\/span><\/strong><\/pre>\n
\u901a\u5e38\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u3092\u4f7f\u7528\u3057\u3066\u78ba\u7387\u306b\u95a2\u3059\u308b\u554f\u984c\u3092\u89e3\u6c7a\u3057\u3088\u3046\u3068\u3059\u308b\u3068\u304d\u306f\u3001 dt<\/strong>\u306e\u4ee3\u308f\u308a\u306bpt<\/b>\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001 dt<\/strong>\u306e\u4fbf\u5229\u306a\u5fdc\u7528\u306f\u3001R \u3067\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8 t \u5206\u5e03\u30d7\u30ed\u30c3\u30c8\u3092\u4f5c\u6210\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u6b21\u306e\u30b3\u30fc\u30c9\u306f\u3001\u3053\u308c\u3092\u884c\u3046\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/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, using 20 degrees of freedom<\/span>\ny <- dt(x = x, df = 20)\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
\u3053\u308c\u306b\u3088\u308a\u3001\u6b21\u306e\u30d7\u30ed\u30c3\u30c8\u304c\u751f\u6210\u3055\u308c\u307e\u3059\u3002<\/span><\/p>\n
\u30dd\u30a4\u30f3\u30c8<\/span><\/strong><\/h2>\n
pt<\/b>\u95a2\u6570\u306f\u3001\u7279\u5b9a\u306e\u78ba\u7387\u5909\u6570x<\/em>\u3068\u81ea\u7531\u5ea6df<\/em>\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u7d2f\u7a4d\u5bc6\u5ea6\u95a2\u6570 (cdf) \u306e\u5024\u3092\u8fd4\u3057\u307e\u3059\u3002 pnorm \u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u306e\u69cb\u6587\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/span><\/p>\n
 pt(x, df)<\/span><\/strong><\/p>\n
\u7c21\u5358\u306b\u8a00\u3046\u3068\u3001 pt \u306f<\/b>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u5185\u306e\u6307\u5b9a\u3055\u308c\u305fx<\/em>\u5024\u306e\u5de6\u5074\u306e\u9818\u57df\u3092\u8fd4\u3057\u307e\u3059\u3002\u7279\u5b9a\u306ex<\/em>\u5024\u306e\u53f3\u5074\u306e\u9818\u57df\u306b\u8208\u5473\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u5f15\u6570lower.tail = FALSE<\/strong>\u3092\u8ffd\u52a0\u3059\u308b\u3060\u3051\u3067\u3059\u3002<\/span><\/p>\n
 pt(x, df, lower.tail = FALSE)<\/span><\/strong><\/p>\n
\u6b21\u306e\u4f8b\u306f\u3001pt \u3092\u4f7f\u7528\u3057\u3066\u3044\u304f\u3064\u304b\u306e\u78ba\u7387\u306e\u554f\u984c\u3092\u89e3\u304f\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n
\u4f8b 1:<\/strong>\u5024\u304c -0.785\u3001\u81ea\u7531\u5ea6\u304c 14 \u306e t \u7d71\u8a08\u91cf\u306e\u5de6\u5074<\/strong>\u306e\u9818\u57df\u3092\u898b\u3064\u3051\u307e\u3059\u3002<\/em><\/span><\/p>\n
 pt(-0.785, 14)\n\n#[1] 0.2227675\n<\/span><\/span><\/strong><\/pre>\n
\u4f8b 2:<\/strong>\u5024\u304c -0.785\u3001\u81ea\u7531\u5ea6\u304c 14 \u306e t \u7d71\u8a08\u91cf\u306e\u53f3\u5074<\/strong>\u306e\u9818\u57df\u3092\u898b\u3064\u3051\u307e\u3059\u3002<\/em><\/span><\/p>\n
 #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#area to the right<\/span>\npt(-0.785, 14, lower.tail = FALSE)\n\n#[1] 0.7772325 \n<\/span><\/span><\/span><\/strong><\/pre>\n
\u4f8b 3:<\/strong> -0.785 \u306e\u5de6\u5074\u307e\u305f\u306f 0.785 \u306e\u53f3\u5074\u306b\u4f4d\u7f6e\u3059\u308b 14 \u81ea\u7531\u5ea6\u306e\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u7dcf\u9762\u7a4d\u3092\u6c42\u3081\u307e\u3059\u3002<\/em><\/span><\/p>\n
 pt (-0.785, 14)<\/span><\/span> + pt (0.785, 14, lower.tail = FALSE)<\/span><\/span>\n\n#[1] 0.4455351<\/strong><\/pre>\n
 qt<\/span><\/strong><\/h2>\n
\u95a2\u6570qt \u306f<\/b>\u3001\u7279\u5b9a\u306e\u78ba\u7387\u5909\u6570x<\/em>\u3068\u81ea\u7531\u5ea6df \u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8 t \u5206\u5e03\u306e\u9006\u7d2f\u7a4d\u5bc6\u5ea6\u95a2\u6570 (cdf) \u306e\u5024\u3092\u8fd4\u3057\u307e\u3059\u3002<\/em> qt \u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u306e\u69cb\u6587\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/span><\/p>\n
 qt(x, df)<\/span><\/strong><\/p>\n
\u7c21\u5358\u306b\u8a00\u3046\u3068\u3001 qt<\/strong>\u3092\u4f7f\u7528\u3057\u3066\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306ep \u756a\u76ee<\/sup>\u306e\u5206\u4f4d\u6570\u306e t \u30b9\u30b3\u30a2\u3092\u8abf\u3079\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n
\u6b21\u306e\u30b3\u30fc\u30c9\u306f\u3001 qt<\/b>\u306e\u52d5\u4f5c\u4f8b\u3092\u3044\u304f\u3064\u304b\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n
 #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\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#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
 qt<\/strong>\u306b\u3088\u3063\u3066\u6c42\u3081\u3089\u308c\u308b\u81e8\u754c\u5024\u306f\u3001t \u5206\u5e03\u8868\u3067\u6c42\u3081\u3089\u308c\u308b\u81e8\u754c\u5024\u3001\u304a\u3088\u3073\u9006 t \u5206\u5e03\u8a08\u7b97\u6a5f\u306b\u3088\u3063\u3066\u6c42\u3081\u3089\u308c\u308b\u81e8\u754c\u5024\u306b\u5bfe\u5fdc\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/span><\/p>\n
 RT<\/span><\/strong><\/h2>\n
\u95a2\u6570rt \u306f\u3001<\/b>\u30d9\u30af\u30c8\u30eb\u9577n<\/em>\u3068\u81ea\u7531\u5ea6df<\/em>\u3092\u6307\u5b9a\u3057\u3066\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u306e\u30d9\u30af\u30c8\u30eb\u3092\u751f\u6210\u3057\u307e\u3059\u3002 rt \u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u306e\u69cb\u6587\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/span><\/p>\n
 rt(n, df)<\/span><\/strong><\/p>\n
\u6b21\u306e\u30b3\u30fc\u30c9\u306f\u3001 rt<\/b>\u306e\u52d5\u4f5c\u4f8b\u3092\u3044\u304f\u3064\u304b\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n
 #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#generate a vector of 1000 random variables that follows a Student t distribution\n#with df = 40\nnarrowDistribution <- rt(1000, 40)\n\n#generate a vector of 1000 random variables that follows a Student t distribution\n#with df = 5\n<\/span>wideDistribution <- rt(1000, 5)\n\n#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
\u3053\u308c\u306b\u3088\u308a\u3001\u6b21\u306e\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u304c\u751f\u6210\u3055\u308c\u307e\u3059\u3002<\/span><\/p>\n
\u5e83\u3044\u5206\u5e03\u304c\u72ed\u3044\u5206\u5e03\u3088\u308a\u3082\u3069\u306e\u3088\u3046\u306b\u5e83\u3044\u304b\u306b\u6ce8\u76ee\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u5b9f\u969b\u3001\u5e83\u3044\u5206\u5e03\u306e\u81ea\u7531\u5ea6\u306f 5 \u3067\u3042\u308b\u306e\u306b\u5bfe\u3057\u3001\u72ed\u3044\u5206\u5e03\u3067\u306f 40 \u3067\u3042\u308b\u3068\u6307\u5b9a\u3057\u307e\u3057\u305f\u3002\u81ea\u7531\u5ea6\u304c\u5c11\u306a\u3044\u307b\u3069\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306f\u5e83\u304f\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n
\u53c2\u8003\u6587\u732e\uff1a
 R \u306e dnorm\u3001pnorm\u3001qnorm\u3001rnorm \u306e\u30ac\u30a4\u30c9<\/a>
R \u306e dbinom\u3001pbinom\u3001qbinom\u3001rbinom \u306e\u30ac\u30a4\u30c9<\/a>
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