{"id":228,"date":"2023-08-03T22:21:12","date_gmt":"2023-08-03T22:21:12","guid":{"rendered":"https:\/\/statorials.org\/nl\/log-normale-verdeling\/"},"modified":"2023-08-03T22:21:12","modified_gmt":"2023-08-03T22:21:12","slug":"log-normale-verdeling","status":"publish","type":"post","link":"https:\/\/statorials.org\/nl\/log-normale-verdeling\/","title":{"rendered":"Lognormale verdeling"},"content":{"rendered":"<p>In dit artikel wordt uitgelegd wat lognormale verdeling in statistieken is. U zult dus ontdekken wat de eigenschappen zijn van de lognormale verdeling en de grafiek van dit type kansverdeling. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-lognormal\"><\/span> Wat is de lognormale verdeling?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De <strong>lognormale verdeling<\/strong> , of <strong>lognormale verdeling<\/strong> , is een kansverdeling die een willekeurige variabele definieert waarvan de logaritme een normale verdeling volgt.<\/p>\n<p> Als de variabele X dus een normale verdeling heeft, heeft de exponenti\u00eble functie ex <sup>x<\/sup> een lognormale verdeling.<\/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-216d8f120f09a37cd8f797bb3b115a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Lognormal}(\\mu,\\sigma^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Merk op dat de lognormale verdeling alleen kan worden gebruikt als de variabelewaarden positief zijn, aangezien de logaritme een functie is die slechts \u00e9\u00e9n positief argument nodig heeft.<\/p>\n<p> Onder de verschillende toepassingen van de lognormale verdeling in de statistiek onderscheiden we het gebruik van deze verdeling om financi\u00eble investeringen te analyseren en betrouwbaarheidsanalyses uit te voeren.<\/p>\n<p> De lognormale verdeling is ook bekend <strong>als de Tinaut-verdeling<\/strong> , soms ook geschreven <strong>als de lognormale verdeling<\/strong> of <strong>log-normale verdeling<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-lognormal\"><\/span> Plot van de lognormale verdeling<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nu we de definitie van de lognormale verdeling kennen, zullen we in deze sectie zien hoe de grafische weergave van de lognormale verdeling varieert afhankelijk van de waarden van het rekenkundig gemiddelde en de standaarddeviatie.<\/p>\n<p> De grafiek van de dichtheidsfunctie van de lognormale verdeling is als volgt: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/trace-de-distribution-lognormale.png\" alt=\"plot van de lognormale verdeling\" class=\"wp-image-4563\" width=\"675\" height=\"406\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Aan de andere kant is de cumulatieve waarschijnlijkheidsgrafiek van de lognormale verdeling als volgt: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-de-probabilite-lognormale-cumulative.png\" alt=\"cumulatieve waarschijnlijkheidsgrafiek van lognormale verdeling\" class=\"wp-image-4564\" width=\"675\" height=\"404\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-lognormal\"><\/span> Kenmerken van de lognormale verdeling<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De lognormale verdeling heeft de volgende kenmerken:<\/p>\n<ul>\n<li> De lognormale verdeling wordt gedefinieerd door de waarde van twee parameters, het rekenkundig gemiddelde \u03bc en de variantie \u03c3 <sup>2<\/sup> .<\/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-216d8f120f09a37cd8f797bb3b115a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Lognormal}(\\mu,\\sigma^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Het domein van de lognormale verdeling bestaat uit positieve re\u00eble getallen, omdat de logaritme geen negatieve of nulwaarden accepteert.<\/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-f543506f97e1f9c5a56ccc4566a3febf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (0,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> De verwachting van een lognormale verdeling is gelijk aan het getal e verhoogd tot de som van het gemiddelde plus de variantie 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-109a1024d530b2993db41f1d7a5a24c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E[X]=e^{\\mu+\\frac{\\sigma^2}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Aan de andere kant kan de variantie van een lognormale verdeling worden berekend met de volgende uitdrukking:<\/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-5afc17462bb71082888ab755626b853a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\left(e^{\\sigma^2}-1\\right)\\cdot e^{2\\mu+\\sigma^2\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"223\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<ul>\n<li> De modus van de lognormale verdeling is equivalent aan het getal e verhoogd tot het gemiddelde van de verdeling.<\/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-21b2bd4c45dca8e305c9ee480d961f4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=e^\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"67\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> De scheefheidsco\u00ebffici\u00ebnt van de lognormale verdeling kan worden bepaald door de volgende formule toe te passen:<\/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-2686fd41c4e28d5c396bf494229a63a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\left(e^{\\sigma^2}+2\\right)\\cdot\\sqrt{e^{\\sigma^2}-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"198\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<ul>\n<li> De formule voor de dichtheidsfunctie van de lognormale verdeling is:<\/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-25698732745689402d16ea353a072cc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{1}{\\sigma \\cdot x\\cdot \\sqrt{2 \\pi}}\\cdot \\exp\\left(-\\frac{(\\ln x-\\mu)^2}{2\\sigma^2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"347\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> De formule voor de cumulatieve waarschijnlijkheidsfunctie van de lognormale verdeling is:<\/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-59c2474703bad4805a6a44bd05cf92bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\Phi\\left(\\frac{\\ln x-\\mu}{\\sigma}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"200\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Goud<\/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-21f36758b04341c7980aa18b13ced720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Phi\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> is de cumulatieve waarschijnlijkheidsfunctie van een <a href=\"https:\/\/statorials.org\/nl\/normale-standaardverdeling\/\">standaard normale verdeling<\/a> .<\/p>\n<ul>\n<li> Het rekenkundig gemiddelde van een lognormale verdeling is groter dan de waarde van de mediaan.<\/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-96e66e8c60e4ce5e235c30258e4ecead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu > Me&#8220; title=&#8220;Rendered by QuickLaTeX.com&#8220; height=&#8220;16&#8243; width=&#8220;61&#8243; style=&#8220;vertical-align: -4px;&#8220;><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In dit artikel wordt uitgelegd wat lognormale verdeling in statistieken is. U zult dus ontdekken wat de eigenschappen zijn van de lognormale verdeling en de grafiek van dit type kansverdeling. Wat is de lognormale verdeling? De lognormale verdeling , of lognormale verdeling , is een kansverdeling die een willekeurige variabele definieert waarvan de logaritme een [&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-228","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>\u25b7 Lognormale verdeling<\/title>\n<meta name=\"description\" content=\"Hier leert u wat lognormale verdeling is, wat de kenmerken zijn van lognormale verdeling en de grafische weergave ervan.\" \/>\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\/log-normale-verdeling\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Lognormale verdeling\" \/>\n<meta property=\"og:description\" content=\"Hier leert u wat lognormale verdeling is, wat de kenmerken zijn van lognormale verdeling en de grafische weergave ervan.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/nl\/log-normale-verdeling\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T22:21:12+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-216d8f120f09a37cd8f797bb3b115a40_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=\"2\u00a0Minuten\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/nl\/log-normale-verdeling\/\",\"url\":\"https:\/\/statorials.org\/nl\/log-normale-verdeling\/\",\"name\":\"\u25b7 Lognormale verdeling\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/nl\/#website\"},\"datePublished\":\"2023-08-03T22:21:12+00:00\",\"dateModified\":\"2023-08-03T22:21:12+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/nl\/#\/schema\/person\/d4b8842173cca1bb62cdec41860e4219\"},\"description\":\"Hier leert u wat lognormale verdeling is, wat de kenmerken zijn van lognormale verdeling en de grafische weergave ervan.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/nl\/log-normale-verdeling\/#breadcrumb\"},\"inLanguage\":\"de\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/nl\/log-normale-verdeling\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/nl\/log-normale-verdeling\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Thuis\",\"item\":\"https:\/\/statorials.org\/nl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Lognormale verdeling\"}]},{\"@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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