{"id":2453,"date":"2023-07-22T05:13:51","date_gmt":"2023-07-22T05:13:51","guid":{"rendered":"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/"},"modified":"2023-07-22T05:13:51","modified_gmt":"2023-07-22T05:13:51","slug":"cdf-w-r-normalnym","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/","title":{"rendered":"Jak u\u017cywa\u0107 normalnego cdf w r (z przyk\u0142adami)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Do pracy z normalnym CDF (funkcj\u0105 rozk\u0142adu skumulowanego) w R mo\u017cna u\u017cy\u0107 nast\u0119puj\u0105cych metod:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Metoda 1: Oblicz normalne prawdopodobie\u0144stwa CDF<\/strong><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate probability that random value is less than 1.96 in normal CDF<\/span>\npnorm(1.96)\n\n<span style=\"color: #008080;\">#calculate probability that random value is greater than 1.96 in normal CDF<\/span>\npnorm(1.96, <span style=\"color: #3366ff;\">lower.tail<\/span> = <span style=\"color: #008000;\">FALSE<\/span> )\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Metoda 2: Wykre\u015bl normalny CDF<\/strong><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define sequence of x-values\n<\/span>x &lt;- seq(-4, 4, .01)\n\n<span style=\"color: #008080;\">#calculate normal CDF probabilities\n<\/span>prob &lt;- pnorm(x)\n \n<span style=\"color: #008080;\">#normal plot CDF\n<\/span>plot(x, prob, type=\" <span style=\"color: #ff0000;\">l<\/span> \")<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Poni\u017csze przyk\u0142ady pokazuj\u0105, jak zastosowa\u0107 te metody w praktyce.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 1: Oblicz<\/strong><\/span> normalne <span style=\"color: #000000;\"><strong>prawdopodobie\u0144stwa<\/strong><\/span> CDF<\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak obliczy\u0107 prawdopodobie\u0144stwo, \u017ce zmienna losowa przyjmie warto\u015b\u0107 mniejsz\u0105 ni\u017c 1,96 w standardowym rozk\u0142adzie normalnym:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate probability that random value is less than 1.96 in normal CDF<\/span>\npnorm(1.96)\n\n[1] 0.9750021\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Prawdopodobie\u0144stwo, \u017ce zmienna losowa przyjmie warto\u015b\u0107 mniejsz\u0105 ni\u017c 1,96 w standardowym rozk\u0142adzie normalnym, wynosi <strong>0,975<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Prawdopodobie\u0144stwo, \u017ce zmienna losowa przyjmie warto\u015b\u0107 wi\u0119ksz\u0105 ni\u017c 1,96, mo\u017cemy r\u00f3wnie\u017c obliczy\u0107, korzystaj\u0105c z argumentu <strong>less.tail<\/strong> :<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate probability that random value is greater than 1.96 in normal CDF<\/span>\npnorm(1.96, <span style=\"color: #3366ff;\">lower.tail<\/span> = <span style=\"color: #008000;\">FALSE<\/span> )\n\n[1] 0.0249979\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Mo\u017cemy u\u017cy\u0107 nast\u0119puj\u0105cej sk\u0142adni, aby znale\u017a\u0107 prawdopodobie\u0144stwo, \u017ce zmienna losowa przyjmie warto\u015b\u0107 pomi\u0119dzy dwiema warto\u015bciami w standardowym rozk\u0142adzie normalnym:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate probability that random value takes on value between -1.96 and 1.96<\/span>\npnorm(1.96) - pnorm(-1.96)\n\n[1] 0.9500042\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Prawdopodobie\u0144stwo, \u017ce zmienna losowa przyjmie warto\u015b\u0107 od -1,96 do 1,96 w standardowym rozk\u0142adzie normalnym, wynosi <strong>0,95<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 2: Wykre\u015blanie normalnego CDF<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak wykre\u015bli\u0107 normalny CDF:<\/span><\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define sequence of x-values\n<\/span>x &lt;- seq(-4, 4, .01)\n\n<span style=\"color: #008080;\">#calculate normal CDF probabilities\n<\/span>prob &lt;- pnorm(x)\n \n<span style=\"color: #008080;\">#normal plot CDF\n<\/span>plot(x, prob, type=\" <span style=\"color: #ff0000;\">l<\/span> \")<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-21963 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normcdf1.png\" alt=\"Normalny wykres CDF w R\" width=\"434\" height=\"398\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">O\u015b x pokazuje warto\u015bci zmiennej losowej zgodnej ze standardowym rozk\u0142adem normalnym, a o\u015b y pokazuje prawdopodobie\u0144stwo, \u017ce zmienna losowa przyjmie warto\u015b\u0107 mniejsz\u0105 ni\u017c warto\u015b\u0107 pokazana na osi x.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad, je\u015bli spojrzymy na x = 1,96, zobaczymy, \u017ce skumulowane prawdopodobie\u0144stwo, \u017ce x jest mniejsze ni\u017c 1,96, wynosi oko\u0142o <strong>0,975:<\/strong><\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-21964 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normalcdf4.png\" alt=\"\" width=\"436\" height=\"400\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Pami\u0119taj, \u017ce mo\u017cesz tak\u017ce zmieni\u0107 estetyk\u0119 normalnego wykresu CDF:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define sequence of x-values\n<\/span>x &lt;- seq(-4, 4, .01)\n\n<span style=\"color: #008080;\">#calculate normal CDF probabilities\n<\/span>prob &lt;- pnorm(x)\n \n<span style=\"color: #008080;\">#normal plot CDF\n<\/span>plot(x, prob, type=' <span style=\"color: #ff0000;\">l<\/span> ', col=' <span style=\"color: #ff0000;\">blue<\/span> ', lwd= <span style=\"color: #008000;\">2<\/span> , main=' <span style=\"color: #ff0000;\">Normal CDF<\/span> ', ylab=' <span style=\"color: #ff0000;\">Cumulative Prob<\/span> ')<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-21965 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normalcdf5.png\" alt=\"\" width=\"437\" height=\"428\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Powi\u0105zane:<\/strong><\/span> <a href=\"https:\/\/statorials.org\/pl\/funkcja-seq-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak u\u017cywa\u0107 funkcji seq w R<\/a><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017csze samouczki wyja\u015bniaj\u0105, jak wykonywa\u0107 inne typowe operacje w j\u0119zyku R:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pl\/wykresl-rozk\u0142ad-normalny-r\/\" target=\"_blank\" rel=\"noopener\">Jak wykre\u015bli\u0107 rozk\u0142ad normalny w R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/wynik-zr\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 wyniki Z w R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/dnorm-pnorm-rnorm-qnorm-w-r\/\" target=\"_blank\" rel=\"noopener\">Przewodnik po dnorm, pnorm, qnorm i rnorm w R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Do pracy z normalnym CDF (funkcj\u0105 rozk\u0142adu skumulowanego) w R mo\u017cna u\u017cy\u0107 nast\u0119puj\u0105cych metod: Metoda 1: Oblicz normalne prawdopodobie\u0144stwa CDF #calculate probability that random value is less than 1.96 in normal CDF pnorm(1.96) #calculate probability that random value is greater than 1.96 in normal CDF pnorm(1.96, lower.tail = FALSE ) Metoda 2: Wykre\u015bl normalny CDF [&hellip;]<\/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-2453","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak u\u017cywa\u0107 normalnego CDF w R (z przyk\u0142adami) \u2013 Statologia<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak u\u017cywa\u0107 normalnego CDF w R, z kilkoma przyk\u0142adami.\" \/>\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\/cdf-w-r-normalnym\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak u\u017cywa\u0107 normalnego CDF w R (z przyk\u0142adami) \u2013 Statologia\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, jak u\u017cywa\u0107 normalnego CDF w R, z kilkoma przyk\u0142adami.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-22T05:13:51+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normcdf1.png\" \/>\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=\"2 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/\",\"url\":\"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/\",\"name\":\"Jak u\u017cywa\u0107 normalnego CDF w R (z przyk\u0142adami) \u2013 Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-22T05:13:51+00:00\",\"dateModified\":\"2023-07-22T05:13:51+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, jak u\u017cywa\u0107 normalnego CDF w R, z kilkoma przyk\u0142adami.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak u\u017cywa\u0107 normalnego cdf w r (z przyk\u0142adami)\"}]},{\"@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. Dzi\u0119ki bogatemu do\u015bwiadczeniu i wiedzy specjalistycznej w dziedzinie statystyki ch\u0119tnie dziel\u0119 si\u0119 swoj\u0105 wiedz\u0105, aby wzmocni\u0107 pozycj\u0119 uczni\u00f3w za po\u015brednictwem Statorials. Wiedzie\u0107 wi\u0119cej\",\"sameAs\":[\"https:\/\/statorials.org\/pl\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Jak u\u017cywa\u0107 normalnego CDF w R (z przyk\u0142adami) \u2013 Statologia","description":"W tym samouczku wyja\u015bniono, jak u\u017cywa\u0107 normalnego CDF w R, z kilkoma przyk\u0142adami.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/","og_locale":"pl_PL","og_type":"article","og_title":"Jak u\u017cywa\u0107 normalnego CDF w R (z przyk\u0142adami) \u2013 Statologia","og_description":"W tym samouczku wyja\u015bniono, jak u\u017cywa\u0107 normalnego CDF w R, z kilkoma przyk\u0142adami.","og_url":"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/","og_site_name":"Statorials","article_published_time":"2023-07-22T05:13:51+00:00","og_image":[{"url":"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normcdf1.png"}],"author":"Benjamin Anderson","twitter_card":"summary_large_image","twitter_misc":{"Napisane przez":"Benjamin Anderson","Szacowany czas czytania":"2 minuty"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/","url":"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/","name":"Jak u\u017cywa\u0107 normalnego CDF w R (z przyk\u0142adami) \u2013 Statologia","isPartOf":{"@id":"https:\/\/statorials.org\/pl\/#website"},"datePublished":"2023-07-22T05:13:51+00:00","dateModified":"2023-07-22T05:13:51+00:00","author":{"@id":"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965"},"description":"W tym samouczku wyja\u015bniono, jak u\u017cywa\u0107 normalnego CDF w R, z kilkoma przyk\u0142adami.","breadcrumb":{"@id":"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/#breadcrumb"},"inLanguage":"pl-PL","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/pl\/cdf-w-r-normalnym\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Dom","item":"https:\/\/statorials.org\/pl\/"},{"@type":"ListItem","position":2,"name":"Jak u\u017cywa\u0107 normalnego cdf w r (z przyk\u0142adami)"}]},{"@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. Dzi\u0119ki bogatemu do\u015bwiadczeniu i wiedzy specjalistycznej w dziedzinie statystyki ch\u0119tnie dziel\u0119 si\u0119 swoj\u0105 wiedz\u0105, aby wzmocni\u0107 pozycj\u0119 uczni\u00f3w za po\u015brednictwem Statorials. Wiedzie\u0107 wi\u0119cej","sameAs":["https:\/\/statorials.org\/pl"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts\/2453","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/comments?post=2453"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts\/2453\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/media?parent=2453"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/categories?post=2453"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/tags?post=2453"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}