{"id":460,"date":"2023-07-29T20:24:26","date_gmt":"2023-07-29T20:24:26","guid":{"rendered":"https:\/\/statorials.org\/cn\/r-%e4%b8%ad%e7%9a%84-dnorm-pnorm-rnorm-qnorm\/"},"modified":"2023-07-29T20:24:26","modified_gmt":"2023-07-29T20:24:26","slug":"r-%e4%b8%ad%e7%9a%84-dnorm-pnorm-rnorm-qnorm","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/r-%e4%b8%ad%e7%9a%84-dnorm-pnorm-rnorm-qnorm\/","title":{"rendered":"R \u4e2d dnorm\u3001pnorm\u3001qnorm \u548c rnorm \u6307\u5357"},"content":{"rendered":"

<\/p>\n

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\u6b63\u6001\u5206\u5e03<\/a>\u662f\u7edf\u8ba1\u5b66\u4e2d\u6700\u5e38\u7528\u7684\u5206\u5e03\u3002\u672c\u6559\u7a0b\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528 R \u4e2d\u7684dnorm<\/strong> \u3001 pnorm<\/strong> \u3001 rnorm<\/strong>\u548cqnorm<\/strong>\u51fd\u6570\u6765\u4f7f\u7528\u6b63\u6001\u5206\u5e03\u3002<\/span><\/p>\n

\u6b63\u5e38\u7684<\/span><\/strong><\/h2>\n

dnorm<\/strong>\u51fd\u6570\u8fd4\u56de\u7ed9\u5b9a\u67d0\u4e2a\u968f\u673a\u53d8\u91cfx<\/em> \u3001\u603b\u4f53\u5e73\u5747\u503c\u03bc<\/em>\u548c\u603b\u4f53\u6807\u51c6\u5dee\u03c3<\/em>\u7684\u6b63\u6001\u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570 (pdf) \u7684\u503c\u3002\u4f7f\u7528 dnorm \u7684\u8bed\u6cd5\u5982\u4e0b\uff1a<\/span><\/p>\n

dnorm(x, \u5747\u503c, \u6807\u51c6\u5dee)<\/span><\/strong><\/p>\n

\u4ee5\u4e0b\u4ee3\u7801\u6f14\u793a\u4e86dnorm<\/strong>\u7684\u4e00\u4e9b\u5b9e\u9645\u793a\u4f8b\uff1a<\/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
\u901a\u5e38\uff0c\u5f53\u5c1d\u8bd5\u4f7f\u7528\u6b63\u6001\u5206\u5e03\u89e3\u51b3\u6709\u5173\u6982\u7387\u7684\u95ee\u9898\u65f6\uff0c\u60a8\u901a\u5e38\u4f1a\u4f7f\u7528pnorm<\/strong>\u800c\u4e0d\u662fdnorm<\/strong> \u3002\u7136\u800c\uff0c dnorm<\/strong>\u7684\u4e00\u4e2a\u6709\u7528\u5e94\u7528\u662f\u5728 R \u4e2d\u521b\u5efa\u6b63\u6001\u5206\u5e03\u56fe\u3002\u4ee5\u4e0b\u4ee3\u7801\u8bf4\u660e\u4e86\u5982\u4f55\u6267\u884c\u6b64\u64cd\u4f5c\uff1a<\/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
\u8fd9\u4f1a\u751f\u6210\u4ee5\u4e0b\u56fe\uff1a<\/span><\/p>\n
\u89c4\u8303<\/span><\/strong><\/h2>\n
pnorm<\/strong>\u51fd\u6570\u8fd4\u56de\u7ed9\u5b9a\u67d0\u4e2a\u968f\u673a\u53d8\u91cfq<\/em> \u3001\u603b\u4f53\u5e73\u5747\u503c\u03bc<\/em>\u548c\u603b\u4f53\u6807\u51c6\u5dee\u03c3<\/em>\u7684\u6b63\u6001\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
 pnorm(q, \u5747\u503c, \u6807\u51c6\u5dee)<\/span><\/strong><\/p>\n
\u7b80\u5355\u6765\u8bf4\uff0c pnorm<\/strong>\u8fd4\u56de\u6b63\u6001\u5206\u5e03\u4e2d\u7ed9\u5b9a\u503cx<\/em>\u5de6\u4fa7\u7684\u9762\u79ef\u3002\u5982\u679c\u60a8\u5bf9\u7ed9\u5b9aq<\/em>\u503c\u53f3\u4fa7\u7684\u533a\u57df\u611f\u5174\u8da3\uff0c\u60a8\u53ef\u4ee5\u7b80\u5355\u5730\u6dfb\u52a0\u53c2\u6570lower.tail = FALSE<\/strong><\/span><\/p>\n
 pnorm(q, \u5e73\u5747\u503c, sd, lower.tail = FALSE)<\/span><\/strong><\/p>\n
\u4ee5\u4e0b\u793a\u4f8b\u8bf4\u660e\u5982\u4f55\u4f7f\u7528 pnorm \u89e3\u51b3\u4e00\u4e9b\u6982\u7387\u95ee\u9898\u3002<\/span><\/p>\n
\u793a\u4f8b 1\uff1a<\/strong>\u5047\u8bbe\u67d0\u6240\u5b66\u6821\u7684\u7537\u751f\u8eab\u9ad8\u670d\u4ece\u6b63\u6001\u5206\u5e03\uff0c\u5e73\u5747\u503c\u4e3a\u03bc<\/span> = 70 \u82f1\u5bf8\uff0c<\/span><\/span><\/span><\/span><\/span>\u6807\u51c6\u5dee\u4e3a\u03c3 = 2 \u82f1\u5bf8\u3002<\/span><\/span><\/span><\/span><\/span><\/em> \u8fd9\u6240\u5b66\u6821\u7684\u7537\u751f\u8eab\u9ad8\u8d85\u8fc7 74 \u82f1\u5bf8\u7684\u6bd4\u4f8b\u5927\u7ea6\u662f\u591a\u5c11\uff1f<\/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
\u5728\u8fd9\u6240\u5b66\u6821\uff0c2,275% \u7684\u7537\u751f\u8eab\u9ad8\u8d85\u8fc7 74 \u82f1\u5bf8\u3002<\/span><\/p>\n
\u793a\u4f8b 2\uff1a<\/strong>\u5047\u8bbe\u67d0\u79cd\u6c34\u736d\u7684\u91cd\u91cf\u670d\u4ece\u6b63\u6001\u5206\u5e03\uff0c\u5e73\u5747\u503c\u4e3a\u03bc<\/span> = 30 \u78c5\uff0c<\/span><\/span><\/span><\/span><\/span>\u6807\u51c6\u5dee\u4e3a\u03c3 = 5 \u78c5\u3002\u8fd9\u79cd\u6c34\u736d\u4e2d\u5927\u7ea6\u6709\u591a\u5c11\u6bd4\u4f8b\u7684\u4f53\u91cd\u4f4e\u4e8e 22 \u78c5\uff1f<\/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
\u8be5\u6c34\u736d\u7269\u79cd\u4e2d\u7ea6 5.4799% \u7684\u4f53\u91cd\u4e0d\u8db3 22 \u78c5\u3002<\/span><\/p>\n
\u793a\u4f8b 3\uff1a<\/strong>\u5047\u8bbe\u67d0\u4e2a\u533a\u57df\u7684\u690d\u7269\u9ad8\u5ea6\u5448\u6b63\u6001\u5206\u5e03\uff0c\u5e73\u5747\u503c\u4e3a\u03bc<\/span> = 13 \u82f1\u5bf8\uff0c<\/span><\/span><\/span><\/span><\/span>\u6807\u51c6\u5dee\u4e3a\u03c3 = 2 \u82f1\u5bf8\u3002\u8be5\u5730\u533a\u5927\u7ea6\u6709\u591a\u5c11\u767e\u5206\u6bd4\u7684\u690d\u7269\u9ad8\u5ea6\u5728 10 \u5230 14 \u82f1\u5bf8\u4e4b\u95f4\uff1f<\/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
\u8be5\u5730\u533a\u7ea6 62.4655% \u7684\u690d\u7269\u9ad8\u5ea6\u5728 10 \u81f3 14 \u82f1\u5bf8\u4e4b\u95f4\u3002<\/span><\/p>\n
 q\u8303\u6570<\/span><\/strong><\/h2>\n
qnorm<\/strong>\u51fd\u6570\u8fd4\u56de\u7ed9\u5b9a\u67d0\u4e2a\u968f\u673a\u53d8\u91cfp<\/em> \u3001\u603b\u4f53\u5e73\u5747\u503c\u03bc<\/em>\u548c\u603b\u4f53\u6807\u51c6\u5dee\u03c3<\/em>\u7684\u6b63\u6001\u5206\u5e03\u7684\u9006\u7d2f\u79ef\u5bc6\u5ea6\u51fd\u6570 (cdf) \u7684\u503c\u3002\u4f7f\u7528 qnorm \u7684\u8bed\u6cd5\u5982\u4e0b\uff1a<\/span><\/p>\n
 qnorm\uff08p\u3001\u5e73\u5747\u503c\u3001\u6807\u51c6\u5dee\uff09<\/span><\/strong><\/p>\n
\u7b80\u5355\u6765\u8bf4\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528qnorm<\/strong>\u627e\u51fa\u6b63\u6001\u5206\u5e03\u7684\u7b2c p \u4e2a\u5206<\/sup>\u4f4d\u6570\u7684 Z \u5206\u6570\u662f\u591a\u5c11\u3002<\/span><\/p>\n
\u4ee5\u4e0b\u4ee3\u7801\u6f14\u793a\u4e86qnorm<\/strong>\u7684\u4e00\u4e9b\u5b9e\u9645\u5e94\u7528\u793a\u4f8b\uff1a<\/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
\u89c4\u8303<\/span><\/strong><\/h2>\n
rnorm<\/strong>\u51fd\u6570\u5728\u7ed9\u5b9a\u5411\u91cf\u957f\u5ea6n<\/em> \u3001\u603b\u4f53\u5e73\u5747\u503c\u03bc<\/em>\u548c\u603b\u4f53\u6807\u51c6\u5dee\u03c3 \u7684<\/em>\u60c5\u51b5\u4e0b\u751f\u6210\u6b63\u6001\u5206\u5e03\u968f\u673a\u53d8\u91cf\u7684\u5411\u91cf\u3002\u4f7f\u7528 rnorm \u7684\u8bed\u6cd5\u5982\u4e0b\uff1a<\/span><\/p>\n
 rnorm(n, \u5e73\u5747\u503c, \u6807\u51c6\u5dee)<\/span><\/strong><\/p>\n
\u4ee5\u4e0b\u4ee3\u7801\u6f14\u793a\u4e86rnorm<\/strong>\u7684\u4e00\u4e9b\u5b9e\u9645\u793a\u4f8b\uff1a<\/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
\u8fd9\u4f1a\u751f\u6210\u4ee5\u4e0b\u76f4\u65b9\u56fe\uff1a<\/span><\/p>\n
\u8bf7\u6ce8\u610f\u5bbd\u5206\u5e03\u6bd4\u7a84\u5206\u5e03\u5bbd\u5f97\u591a\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u6307\u5b9a\u5bbd\u5206\u5e03\u4e2d\u7684\u6807\u51c6\u5dee\u4e3a 25\uff0c\u800c\u7a84\u5206\u5e03\u4e2d\u7684\u6807\u51c6\u5dee\u4ec5\u4e3a 15\u3002\u53e6\u8bf7\u6ce8\u610f\uff0c\u4e24\u4e2a\u76f4\u65b9\u56fe\u5747\u4ee5 50 \u7684\u5e73\u5747\u503c\u4e3a\u4e2d\u5fc3\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
\u6b63\u6001\u5206\u5e03\u662f\u7edf\u8ba1\u5b66\u4e2d\u6700\u5e38\u7528\u7684\u5206\u5e03\u3002\u672c\u6559\u7a0b\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528 R \u4e2d\u7684dnorm \u3001 pnorm \u3001 rnorm\u548cqno […]<\/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-460","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"\nR \u4e2d dnorm\u3001pnorm\u3001qnorm \u548c rnorm \u6307\u5357 - Statorials<\/title>\n<meta name=\"description\" content=\"R \u4e2d dnorm\u3001pnorm\u3001rnorm \u548c qnorm \u51fd\u6570\u7684\u7b80\u5355\u6307\u5357\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/cn\/r-\u4e2d\u7684-dnorm-pnorm-rnorm-qnorm\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R \u4e2d dnorm\u3001pnorm\u3001qnorm \u548c rnorm \u6307\u5357 - 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