{"id":229,"date":"2023-08-03T22:21:12","date_gmt":"2023-08-03T22:21:12","guid":{"rendered":"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/"},"modified":"2023-08-03T22:21:12","modified_gmt":"2023-08-03T22:21:12","slug":"mencatat-distribusi-normal","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/","title":{"rendered":"Distribusi lognormal"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi lognormal dalam statistik. Jadi, Anda akan mengetahui apa saja sifat-sifat distribusi lognormal dan grafik dari jenis distribusi probabilitas tersebut. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-lognormal\"><\/span> Apa distribusi lognormalnya?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Distribusi lognormal<\/strong> , atau <strong>distribusi lognormal<\/strong> , adalah distribusi probabilitas yang mendefinisikan variabel acak yang logaritmanya mengikuti distribusi normal.<\/p>\n<p> Oleh karena itu, jika variabel X berdistribusi normal, maka fungsi eksponensial e <sup>x<\/sup> berdistribusi lognormal.<\/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> Perhatikan bahwa distribusi lognormal hanya dapat digunakan jika nilai variabelnya positif, karena logaritma adalah fungsi yang hanya mengambil satu argumen positif.<\/p>\n<p> Di antara berbagai penerapan distribusi lognormal dalam statistik, kami membedakan penggunaan distribusi ini untuk menganalisis investasi keuangan dan melakukan analisis keandalan.<\/p>\n<p> Distribusi lognormal dikenal juga <strong>sebagai distribusi Tinaut<\/strong> , terkadang juga ditulis <strong>sebagai distribusi lognormal<\/strong> atau <strong>distribusi log-normal<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-lognormal\"><\/span> Plot distribusi lognormal<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sekarang setelah kita mengetahui definisi distribusi lognormal, pada bagian ini kita akan melihat bagaimana representasi grafis dari distribusi lognormal bervariasi tergantung pada nilai mean aritmatika dan deviasi standarnya.<\/p>\n<p> Grafik fungsi densitas distribusi lognormal adalah sebagai berikut: <\/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 distribusi lognormal\" class=\"wp-image-4563\" width=\"675\" height=\"406\" srcset=\"\" sizes=\"\"><\/figure>\n<p> Sedangkan grafik probabilitas kumulatif dari distribusi lognormal adalah sebagai berikut: <\/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=\"plot probabilitas kumulatif dari distribusi lognormal\" class=\"wp-image-4564\" width=\"675\" height=\"404\" srcset=\"\" sizes=\"\"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-lognormal\"><\/span> Ciri-ciri distribusi lognormal<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Distribusi lognormal mempunyai ciri-ciri sebagai berikut:<\/p>\n<ul>\n<li> Distribusi lognormal ditentukan oleh nilai dua parameter, rata-rata aritmatikanya \u03bc dan variansnya \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> Domain distribusi lognormal terdiri dari bilangan real positif, karena logaritma tidak menerima nilai negatif atau nol.<\/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> Ekspektasi distribusi lognormal sama dengan angka e yang dipangkatkan dari jumlah mean ditambah varians dibagi dua.<\/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> Di sisi lain, varians dari distribusi lognormal dapat dihitung dengan ekspresi berikut:<\/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> Modus distribusi lognormal ekuivalen dengan bilangan e yang dipangkatkan ke mean distribusi.<\/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> Koefisien skewness distribusi lognormal dapat ditentukan dengan menggunakan rumus berikut:<\/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> Rumus fungsi kepadatan berdistribusi lognormal adalah:<\/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> Rumus fungsi probabilitas kumulatif dari distribusi lognormal adalah:<\/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> Emas<\/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> adalah fungsi probabilitas kumulatif dari <a href=\"https:\/\/statorials.org\/id\/distribusi-standar-normal\/\">distribusi normal standar<\/a> .<\/p>\n<ul>\n<li> Rata-rata aritmatika suatu distribusi lognormal lebih besar dari nilai mediannya.<\/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&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;16&#8243; width=&#8221;61&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi lognormal dalam statistik. Jadi, Anda akan mengetahui apa saja sifat-sifat distribusi lognormal dan grafik dari jenis distribusi probabilitas tersebut. Apa distribusi lognormalnya? Distribusi lognormal , atau distribusi lognormal , adalah distribusi probabilitas yang mendefinisikan variabel acak yang logaritmanya mengikuti distribusi normal. Oleh karena itu, jika variabel X berdistribusi normal, [&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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Distribusi lognormal<\/title>\n<meta name=\"description\" content=\"Di sini Anda akan mempelajari apa itu distribusi lognormal, apa saja ciri-ciri distribusi lognormal dan representasi grafisnya.\" \/>\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\/id\/mencatat-distribusi-normal\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Distribusi lognormal\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan mempelajari apa itu distribusi lognormal, apa saja ciri-ciri distribusi lognormal dan representasi grafisnya.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/\" \/>\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=\"Benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/\",\"url\":\"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/\",\"name\":\"\u25b7 Distribusi lognormal\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-08-03T22:21:12+00:00\",\"dateModified\":\"2023-08-03T22:21:12+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Di sini Anda akan mempelajari apa itu distribusi lognormal, apa saja ciri-ciri distribusi lognormal dan representasi grafisnya.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribusi lognormal\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/id\/#website\",\"url\":\"https:\/\/statorials.org\/id\/\",\"name\":\"Statorials\",\"description\":\"Panduan anda untuk kompetensi statistik!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\",\"name\":\"Benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin anderson\"},\"description\":\"Halo, saya Benjamin, pensiunan profesor statistika yang menjadi guru Statorial yang berdedikasi. Dengan pengalaman dan keahlian yang luas di bidang statistika, saya ingin berbagi ilmu untuk memberdayakan mahasiswa melalui Statorials. Baca selengkapnya\",\"sameAs\":[\"http:\/\/statorials.org\/id\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u25b7 Distribusi lognormal","description":"Di sini Anda akan mempelajari apa itu distribusi lognormal, apa saja ciri-ciri distribusi lognormal dan representasi grafisnya.","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\/id\/mencatat-distribusi-normal\/","og_locale":"id_ID","og_type":"article","og_title":"\u25b7 Distribusi lognormal","og_description":"Di sini Anda akan mempelajari apa itu distribusi lognormal, apa saja ciri-ciri distribusi lognormal dan representasi grafisnya.","og_url":"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/","og_site_name":"Statorials","article_published_time":"2023-08-03T22:21:12+00:00","og_image":[{"url":"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-216d8f120f09a37cd8f797bb3b115a40_l3.png"}],"author":"Benjamin anderson","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Benjamin anderson","Estimasi waktu membaca":"1 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/","url":"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/","name":"\u25b7 Distribusi lognormal","isPartOf":{"@id":"https:\/\/statorials.org\/id\/#website"},"datePublished":"2023-08-03T22:21:12+00:00","dateModified":"2023-08-03T22:21:12+00:00","author":{"@id":"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81"},"description":"Di sini Anda akan mempelajari apa itu distribusi lognormal, apa saja ciri-ciri distribusi lognormal dan representasi grafisnya.","breadcrumb":{"@id":"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/#breadcrumb"},"inLanguage":"id","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/id\/mencatat-distribusi-normal\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/statorials.org\/id\/"},{"@type":"ListItem","position":2,"name":"Distribusi lognormal"}]},{"@type":"WebSite","@id":"https:\/\/statorials.org\/id\/#website","url":"https:\/\/statorials.org\/id\/","name":"Statorials","description":"Panduan anda untuk kompetensi statistik!","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/statorials.org\/id\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"id"},{"@type":"Person","@id":"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81","name":"Benjamin anderson","image":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/statorials.org\/id\/#\/schema\/person\/image\/","url":"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg","contentUrl":"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg","caption":"Benjamin anderson"},"description":"Halo, saya Benjamin, pensiunan profesor statistika yang menjadi guru Statorial yang berdedikasi. Dengan pengalaman dan keahlian yang luas di bidang statistika, saya ingin berbagi ilmu untuk memberdayakan mahasiswa melalui Statorials. Baca selengkapnya","sameAs":["http:\/\/statorials.org\/id"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/id\/wp-json\/wp\/v2\/posts\/229"}],"collection":[{"href":"https:\/\/statorials.org\/id\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/id\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/id\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/id\/wp-json\/wp\/v2\/comments?post=229"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/id\/wp-json\/wp\/v2\/posts\/229\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/id\/wp-json\/wp\/v2\/media?parent=229"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/id\/wp-json\/wp\/v2\/categories?post=229"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/id\/wp-json\/wp\/v2\/tags?post=229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}