{"id":457,"date":"2023-07-29T20:24:26","date_gmt":"2023-07-29T20:24:26","guid":{"rendered":"https:\/\/statorials.org\/pl\/dnorm-pnorm-rnorm-qnorm-w-r\/"},"modified":"2023-07-29T20:24:26","modified_gmt":"2023-07-29T20:24:26","slug":"dnorm-pnorm-rnorm-qnorm-w-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/dnorm-pnorm-rnorm-qnorm-w-r\/","title":{"rendered":"Przewodnik po dnorm, pnorm, qnorm i rnorm w r"},"content":{"rendered":"

<\/p>\n

\n

Rozk\u0142ad normalny<\/a> jest najcz\u0119\u015bciej u\u017cywanym rozk\u0142adem w statystyce. W tym samouczku wyja\u015bniono, jak u\u017cywa\u0107 rozk\u0142adu normalnego w j\u0119zyku R przy u\u017cyciu funkcji dnorm<\/strong> , pnorm<\/strong> , rnorm<\/strong> i qnorm<\/strong> .<\/span><\/p>\n

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

Funkcja dnorm<\/strong> zwraca warto\u015b\u0107 funkcji g\u0119sto\u015bci prawdopodobie\u0144stwa (pdf) rozk\u0142adu normalnego, bior\u0105c pod uwag\u0119 pewn\u0105 zmienn\u0105 losow\u0105 x<\/em> , \u015bredni\u0105 populacji \u03bc<\/em> i odchylenie standardowe populacji \u03c3<\/em> . Sk\u0142adnia u\u017cywania dnorm jest nast\u0119puj\u0105ca:<\/span><\/p>\n

dnorm(x, \u015brednia, sd)<\/span><\/strong><\/p>\n

Poni\u017cszy kod demonstruje kilka przyk\u0142ad\u00f3w dnorm<\/strong> w akcji:<\/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
 Zazwyczaj, pr\u00f3buj\u0105c rozwi\u0105za\u0107 pytania dotycz\u0105ce prawdopodobie\u0144stwa przy u\u017cyciu rozk\u0142adu normalnego, cz\u0119sto u\u017cywasz pnorm<\/strong> zamiast dnorm<\/strong> . Przydatnym zastosowaniem dnorm<\/strong> jest jednak utworzenie wykresu rozk\u0142adu normalnego w R. Poni\u017cszy kod ilustruje, jak to zrobi\u0107:<\/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
 Generuje to nast\u0119puj\u0105cy wykres:<\/span><\/p>\n
 norma<\/span><\/strong><\/h2>\n
 Funkcja pnorm<\/strong> zwraca warto\u015b\u0107 funkcji g\u0119sto\u015bci skumulowanej (cdf) rozk\u0142adu normalnego, bior\u0105c pod uwag\u0119 pewn\u0105 zmienn\u0105 losow\u0105 q<\/em> , \u015bredni\u0105 populacji \u03bc<\/em> i odchylenie standardowe populacji \u03c3<\/em> . Sk\u0142adnia u\u017cywania pnorm jest nast\u0119puj\u0105ca:<\/span><\/p>\n
 pnorm(q, \u015brednia, sd)<\/span><\/strong><\/p>\n
 M\u00f3wi\u0105c najpro\u015bciej, pnorm<\/strong> zwraca obszar na lewo od danej warto\u015bci x<\/em> w rozk\u0142adzie normalnym. Je\u015bli interesuje Ci\u0119 obszar na prawo od danej warto\u015bci q<\/em> , mo\u017cesz po prostu doda\u0107 argument less.tail = FALSE<\/strong><\/span><\/p>\n
 pnorm(q, \u015brednia, sd, ni\u017csza.ogon = FA\u0141SZ)<\/span><\/strong><\/p>\n
 Poni\u017csze przyk\u0142ady ilustruj\u0105, jak rozwi\u0105za\u0107 niekt\u00f3re pytania dotycz\u0105ce prawdopodobie\u0144stwa za pomoc\u0105 pnorm.<\/span><\/p>\n
 Przyk\u0142ad 1:<\/strong> Za\u0142\u00f3\u017cmy, \u017ce wzrost m\u0119\u017cczyzn w pewnej szkole ma rozk\u0142ad normalny ze \u015bredni\u0105 \u03bc<\/span> = 70 cali i<\/span><\/span><\/span><\/span><\/span> odchyleniem standardowym \u03c3 = 2 cale.<\/span><\/span><\/span><\/span><\/span><\/em> Jaki procent m\u0119\u017cczyzn w tej szkole ma w przybli\u017ceniu ponad 74 cale wzrostu?<\/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
 W tej szkole 2275% m\u0119\u017cczyzn ma ponad 74 cale wzrostu.<\/span><\/p>\n
 Przyk\u0142ad 2:<\/strong> Za\u0142\u00f3\u017cmy, \u017ce masa pewnego gatunku wydry ma rozk\u0142ad normalny ze \u015bredni\u0105 \u03bc<\/span> = 30 funt\u00f3w i<\/span><\/span><\/span><\/span><\/span> odchyleniem standardowym \u03c3 = 5 funt\u00f3w. Jaki procent wydr tego gatunku w przybli\u017ceniu wa\u017cy mniej ni\u017c 22 funty?<\/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
 Oko\u0142o 5,4799% tego gatunku wydry wa\u017cy mniej ni\u017c 22 funty.<\/span><\/p>\n
 Przyk\u0142ad 3:<\/strong> Za\u0142\u00f3\u017cmy, \u017ce wysoko\u015b\u0107 ro\u015blin w pewnym regionie ma rozk\u0142ad normalny ze \u015bredni\u0105 \u03bc<\/span> = 13 cali i<\/span><\/span><\/span><\/span><\/span> odchyleniem standardowym \u03c3 = 2 cale. Jaki procent ro\u015blin w tym regionie ma w przybli\u017ceniu wysoko\u015b\u0107 od 10 do 14 cali?<\/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
 Oko\u0142o 62,4655% ro\u015blin w tym regionie ma wysoko\u015b\u0107 od 10 do 14 cali.<\/span><\/p>\n
 qnorma<\/span><\/strong><\/h2>\n
 Funkcja qnorm<\/strong> zwraca warto\u015b\u0107 odwrotnej funkcji g\u0119sto\u015bci skumulowanej (cdf) rozk\u0142adu normalnego, bior\u0105c pod uwag\u0119 pewn\u0105 zmienn\u0105 losow\u0105 p<\/em> , \u015bredni\u0105 populacji \u03bc<\/em> i odchylenie standardowe populacji \u03c3<\/em> . Sk\u0142adnia u\u017cycia qnorm jest nast\u0119puj\u0105ca:<\/span><\/p>\n
 qnorm (p, \u015brednia, sd)<\/span><\/strong><\/p>\n
 M\u00f3wi\u0105c pro\u015bciej, mo\u017cesz u\u017cy\u0107 qnorm<\/strong> , aby dowiedzie\u0107 si\u0119, jaki jest wynik Z p-tego kwantyla<\/sup> rozk\u0142adu normalnego.<\/span><\/p>\n
 Poni\u017cszy kod demonstruje kilka przyk\u0142ad\u00f3w qnorm<\/strong> w akcji:<\/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
 rnorm<\/span><\/strong><\/h2>\n
 Funkcja rnorm<\/strong> generuje wektor zmiennych losowych o rozk\u0142adzie normalnym, maj\u0105c d\u0142ugo\u015b\u0107 wektora n<\/em> , \u015bredni\u0105 populacji \u03bc<\/em> i odchylenie standardowe populacji \u03c3<\/em> . Sk\u0142adnia u\u017cywania rnorm jest nast\u0119puj\u0105ca:<\/span><\/p>\n
 rnorm(n, \u015brednia, sd)<\/span><\/strong><\/p>\n
 Poni\u017cszy kod demonstruje kilka przyk\u0142ad\u00f3w rnorm<\/strong> w akcji:<\/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
 Generuje to nast\u0119puj\u0105ce histogramy:<\/span><\/p>\n
 Zwr\u00f3\u0107 uwag\u0119, \u017ce szeroka dystrybucja jest znacznie szersza ni\u017c w\u0105ska dystrybucja. Rzeczywi\u015bcie okre\u015blili\u015bmy, \u017ce odchylenie standardowe w szerokim rozk\u0142adzie wynosi\u0142o 25, w por\u00f3wnaniu z zaledwie 15 w w\u0105skim rozk\u0142adzie. Nale\u017cy r\u00f3wnie\u017c zauwa\u017cy\u0107, \u017ce oba histogramy s\u0105 wy\u015brodkowane wok\u00f3\u0142 \u015bredniej 50.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
Rozk\u0142ad normalny jest najcz\u0119\u015bciej u\u017cywanym rozk\u0142adem w statystyce. W tym samouczku wyja\u015bniono, jak u\u017cywa\u0107 rozk\u0142adu normalnego w j\u0119zyku R przy u\u017cyciu funkcji dnorm , pnorm , rnorm i qnorm . okropne Funkcja dnorm zwraca warto\u015b\u0107 funkcji g\u0119sto\u015bci prawdopodobie\u0144stwa (pdf) rozk\u0142adu normalnego, bior\u0105c pod uwag\u0119 pewn\u0105 zmienn\u0105 losow\u0105 x , \u015bredni\u0105 populacji \u03bc i odchylenie standardowe […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-457","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"\nPrzewodnik po dnorm, pnorm, qnorm i rnorm w R - Statorials<\/title>\n<meta name=\"description\" content=\"Prosty przewodnik po funkcjach dnorm, pnorm, rnorm i qnorm w R.\" \/>\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\/pl\/dnorm-pnorm-rnorm-qnorm-w-r\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Przewodnik po dnorm, pnorm, qnorm i rnorm w R - Statorials\" \/>\n<meta property=\"og:description\" content=\"Prosty przewodnik po funkcjach dnorm, pnorm, rnorm i qnorm w R.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/dnorm-pnorm-rnorm-qnorm-w-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T20:24:26+00:00\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minut\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/dnorm-pnorm-rnorm-qnorm-w-r\/\",\"url\":\"https:\/\/statorials.org\/pl\/dnorm-pnorm-rnorm-qnorm-w-r\/\",\"name\":\"Przewodnik po dnorm, pnorm, qnorm i rnorm w R - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-29T20:24:26+00:00\",\"dateModified\":\"2023-07-29T20:24:26+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Prosty przewodnik po funkcjach dnorm, pnorm, rnorm i qnorm w R.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/dnorm-pnorm-rnorm-qnorm-w-r\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/dnorm-pnorm-rnorm-qnorm-w-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/dnorm-pnorm-rnorm-qnorm-w-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Przewodnik po dnorm, pnorm, qnorm i rnorm w r\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pl\/#website\",\"url\":\"https:\/\/statorials.org\/pl\/\",\"name\":\"Statorials\",\"description\":\"Tw\u00f3j przewodnik po kompetencjach statystycznych!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pl-PL\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pl-PL\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. 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