{"id":226,"date":"2023-08-03T23:08:41","date_gmt":"2023-08-03T23:08:41","guid":{"rendered":"https:\/\/statorials.org\/nl\/uniforme-continue-distributie\/"},"modified":"2023-08-03T23:08:41","modified_gmt":"2023-08-03T23:08:41","slug":"uniforme-continue-distributie","status":"publish","type":"post","link":"https:\/\/statorials.org\/nl\/uniforme-continue-distributie\/","title":{"rendered":"Uniforme en continue distributie"},"content":{"rendered":"<p>In dit artikel wordt uitgelegd wat continue uniforme distributie is en waarvoor het wordt gebruikt. Je vindt er ook de grafiek van de continue uniforme verdeling en de eigenschappen van dit type verdeling. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-uniforme-continua\"><\/span> Wat is een continue uniforme verdeling?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De <strong>continue uniforme verdeling<\/strong> is een soort kansverdeling waarbij alle waarden dezelfde kans hebben om te voorkomen. Met andere woorden: de continue uniforme verdeling is een verdeling waarbij de waarschijnlijkheid uniform verdeeld is over een interval.<\/p>\n<p> De continue uniforme verdeling wordt gebruikt om continue variabelen te beschrijven die een constante waarschijnlijkheid hebben. Op dezelfde manier wordt continue uniforme verdeling gebruikt om willekeurige processen te defini\u00ebren, omdat als alle uitkomsten dezelfde waarschijnlijkheid hebben, dit betekent dat er willekeur in de uitkomst zit.<\/p>\n<p> De continue uniforme verdeling heeft twee karakteristieke parameters, <em>a<\/em> en <em>b<\/em> , die het equiprobabiliteitsinterval defini\u00ebren. Het symbool voor de continue uniforme verdeling is dus <em>U(a,b)<\/em> , waarbij <em>a<\/em> en <em>b<\/em> de karakteristieke waarden van de verdeling zijn.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-339036da3788f71282d3936dd092730c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim U(a,b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Als de uitkomst van een willekeurig experiment bijvoorbeeld elke waarde tussen 5 en 9 kan aannemen en alle mogelijke uitkomsten dezelfde waarschijnlijkheid hebben om te voorkomen, kan het experiment worden gesimuleerd met een continue uniforme verdeling U(5.9).<\/p>\n<p> De continue uniforme verdeling wordt ook wel <strong>rechthoekige verdeling<\/strong> genoemd. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-uniforme-continua\"><\/span> Formule voor continue uniforme verdeling<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De dichtheidsfunctie die de waarschijnlijkheid van een uniforme verdeling definieert, is die gedeeld door het verschil tussen <em>b<\/em> en <em>a<\/em> . Daarom is de <strong>formule voor de continue uniforme verdeling<\/strong> :<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f28c4a144fb1377061b84b56968c9540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim U(a,b)\\\\[2ex]f(x)=\\cfrac{1}{b-a}\\\\[4ex]x\\in [a,b]\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"123\" width=\"99\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Aan de andere kant wordt de cumulatieve waarschijnlijkheidsfunctie van de continue uniforme verdeling gedefinieerd door de volgende uitdrukking:<\/p>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\displaystyle F(x)=\\left\\{\\begin{array}{ll}0&amp;\\text{si }x&lt;h2 class=\"wp-block-heading\"&gt;&lt;span class=\"ez-toc-section\" id =\"grafica-de-la-distribucion-uniforme-continua\"&gt;&lt;\/span&gt; Graph of continuous uniform distribution&lt;span class=\"ez-toc-section-end\"&gt;&lt;\/span&gt;&lt;\/h2&gt; Since in a distribution uniform continuous probability is constant, its graphical representation is simply a function with a constant value defined in the same interval as the uniform distribution. &lt;figure class=\"wp-block-image aligncenter size-full is-resized\"&gt;&lt;img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/ 08\/distribution-uniforme-continue.png\" alt=\"Continuous uniform distribution graph\" class=\"wp-image-4498\" width=\"330\" height=\"232\" srcset=\"\" sizes=\"\"&gt;&lt;\/figure &gt; On the other hand, the cumulative probability graph of the continuous uniform distribution is as follows: &lt;figure class=\"wp-block-image aligncenter size-full is-resized\"&gt;&lt;img decoding=\"async\" loading=\"lazy \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-uniforme-continue-probabilite-cumulative.png\" alt=\"cumulative probability plot of a continuous uniform distribution\" class= \"wp-image-4499\" width=\"247\" height=\"193\" srcset=\"\" sizes=\"\"&gt;&lt;\/figure&gt;&lt;h2 class=\"wp-block-heading\"&gt;&lt;span class=\"ez-toc -section\" id=\"caracteristicas-de-la-distribucion-uniforme-continua\"&gt;&lt;\/span&gt; Characteristics of the continuous uniform distribution&lt;span class=\"ez-toc-section-end\"&gt;&lt;\/span&gt;&lt;\/h2 &gt; The continuous uniform distribution has the following characteristics: &lt;ul&gt;&lt;li&gt; The continuous uniform distribution is defined by two real parameters, &lt;em&gt;a&lt;\/em&gt; and &lt;em&gt;b&lt;\/em&gt;, which establish the limits in which the probability is constant.&lt;\/li&gt;&lt;\/ul&gt;[latex]a,b\\in \\mathbb{R}\n\n***Error message:\nPlease use \\mathaccent for accents in math mode.\nleading text: ...continuous uniform distribution probability\nPlease use \\mathaccent for accents in math mode.\nleading text: ...if the probability is constant, its representation\nPlease use \\mathaccent for accents in math mode.\nleading text: ...a function with a constant value de\nPlease use \\mathaccent for accents in math mode.\nleading text: ...c a constant value defined in the same\nPlease use \\mathaccent for accents in math mode.\nleading text: ...On the other hand, the probability graph\nPlease use \\mathaccent for accents in math mode.\nleading text: ... part, the cumulative probability graph\nPlease use \\mathaccent for accents in math mode.\nleading text: ...nue-probabilite-cumulative.png\" alt=\"plot\n\n<\/pre>\n<ul>\n<li> De continue uniforme verdeling kan alleen waarden aannemen die zich bevinden in het interval gevormd door <em>a<\/em> en <em>b<\/em> inclusief.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3d713e1ad32e4d969c10e514cd71b7d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in [a,b]\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Het gemiddelde van een continue uniforme verdeling is gelijk aan de som van de twee karakteristieke parameters gedeeld door twee.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-96d92a77b5dce5d38b2b2f3b79ac09a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{a+b}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"105\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> De variantie van een continue uniforme verdeling is gelijk aan het kwadraat van het verschil tussen <em>b<\/em> en <em>a<\/em> gedeeld door twaalf.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1f52c10cdd7fb59fca29f8d7703e7495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{(b-a)^2}{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"149\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> De mediaan van een continue uniforme verdeling valt samen met het gemiddelde en wordt daarom berekend met dezelfde formule:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9acd8c7117f5765f6e47060148e541e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Me=\\cfrac{a+b}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"92\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> De continue uniforme verdeling is symmetrisch, daarom is de asymmetrieco\u00ebffici\u00ebnt van dit type verdeling nul.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f32c2fb2ba717dc1c88c67cb82c26e9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"46\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> De kurtosis van een continue uniforme verdeling is niet afhankelijk van de parameters, deze is altijd -6 gedeeld door 5.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-53318cb30ff0697fd742850c405c7545_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C=\\cfrac{-6}{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"71\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> De standaard uniforme verdeling is die continue uniforme verdeling waarvan de parameters <em>a<\/em> en <em>b<\/em> respectievelijk 0 en 1 zijn. <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-be2dbf7d29ed8c8a1220e74498c77d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim U(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-uniforme-continua-y-distribucion-uniforme-discreta\"><\/span> Continue uniforme distributie en discrete uniforme distributie<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ten slotte zullen we zien wat het verschil is tussen de continue uniforme verdeling en de discrete uniforme verdeling, aangezien het twee waarschijnlijkheidsverdelingen zijn die verward kunnen worden, maar die totaal verschillende concepten vertegenwoordigen.<\/p>\n<p> Het belangrijkste <strong>verschil tussen een continue uniforme verdeling en een discrete uniforme verdeling<\/strong> zijn de waarden die ze kunnen aannemen. Een continue uniforme verdeling wordt gedefinieerd in een continue monsterruimte, terwijl een discrete uniforme verdeling wordt gedefinieerd in een discrete monsterruimte.<\/p>\n<p> Daarom kan de discrete uniforme verdeling slechts enkele waarden in een interval aannemen, meestal gehele getallen, terwijl een continue uniforme verdeling elke waarde in een interval kan aannemen, inclusief decimale getallen. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Zie:<\/strong> <a href=\"https:\/\/statorials.org\/nl\/discrete-uniforme-verdeling\/\">Discrete uniforme verdeling<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>In dit artikel wordt uitgelegd wat continue uniforme distributie is en waarvoor het wordt gebruikt. Je vindt er ook de grafiek van de continue uniforme verdeling en de eigenschappen van dit type verdeling. Wat is een continue uniforme verdeling? De continue uniforme verdeling is een soort kansverdeling waarbij alle waarden dezelfde kans hebben om te [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-226","post","type-post","status-publish","format-standard","hentry","category-waarschijnlijkheid"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7Continue uniforme verdeling<\/title>\n<meta name=\"description\" content=\"Hier vindt u wat continue uniforme verdeling is, de formule, grafiek en kenmerken van continue uniforme verdeling.\" \/>\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\/nl\/uniforme-continue-distributie\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7Continue uniforme verdeling\" \/>\n<meta property=\"og:description\" content=\"Hier vindt u wat continue uniforme verdeling is, de formule, grafiek en kenmerken van continue uniforme verdeling.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/nl\/uniforme-continue-distributie\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T23:08:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-339036da3788f71282d3936dd092730c_l3.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Verfasst von\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Gesch\u00e4tzte Lesezeit\" \/>\n\t<meta name=\"twitter:data2\" content=\"4\u00a0Minuten\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/nl\/uniforme-continue-distributie\/\",\"url\":\"https:\/\/statorials.org\/nl\/uniforme-continue-distributie\/\",\"name\":\"\u25b7Continue uniforme verdeling\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/nl\/#website\"},\"datePublished\":\"2023-08-03T23:08:41+00:00\",\"dateModified\":\"2023-08-03T23:08:41+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/nl\/#\/schema\/person\/d4b8842173cca1bb62cdec41860e4219\"},\"description\":\"Hier vindt u wat continue uniforme verdeling is, de formule, grafiek en kenmerken van continue uniforme verdeling.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/nl\/uniforme-continue-distributie\/#breadcrumb\"},\"inLanguage\":\"de\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/nl\/uniforme-continue-distributie\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/nl\/uniforme-continue-distributie\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Thuis\",\"item\":\"https:\/\/statorials.org\/nl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Uniforme en continue distributie\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/nl\/#website\",\"url\":\"https:\/\/statorials.org\/nl\/\",\"name\":\"Statorials\",\"description\":\"Uw gids voor statistische competentie\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/nl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"de\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/nl\/#\/schema\/person\/d4b8842173cca1bb62cdec41860e4219\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"de\",\"@id\":\"https:\/\/statorials.org\/nl\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/nl\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/nl\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Ik ben Benjamin, een gepensioneerde hoogleraar statistiek die nu een toegewijde Statorials-lesgever is. 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