{"id":231,"date":"2023-08-03T21:54:17","date_gmt":"2023-08-03T21:54:17","guid":{"rendered":"https:\/\/statorials.org\/id\/hukum-pareto\/"},"modified":"2023-08-03T21:54:17","modified_gmt":"2023-08-03T21:54:17","slug":"hukum-pareto","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/hukum-pareto\/","title":{"rendered":"Distribusi pareto"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi Pareto dalam statistik dan kegunaannya. Anda juga akan dapat melihat grafik distribusi Pareto dan properti dari jenis distribusi probabilitas ini. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-de-pareto\"><\/span> Apa itu distribusi Pareto?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Distribusi Pareto<\/strong> adalah distribusi probabilitas kontinu yang digunakan dalam statistik untuk memodelkan prinsip Pareto. Oleh karena itu, distribusi Pareto merupakan distribusi probabilitas yang memiliki beberapa nilai yang probabilitas terjadinya jauh lebih tinggi dibandingkan nilai lainnya.<\/p>\n<p> Ingatlah bahwa hukum Pareto, disebut juga aturan 80-20, adalah prinsip statistik yang menyatakan bahwa sebagian besar penyebab suatu fenomena disebabkan oleh sebagian kecil populasi.<\/p>\n<p> Distribusi Pareto mempunyai dua parameter karakteristik: parameter skala x <sub>m<\/sub> dan parameter bentuk \u03b1.<\/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-c13a66a388e0a7e26781a0e8d9645f40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Pareto}(\\alpha,x_m)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Awalnya, distribusi Pareto digunakan untuk menggambarkan distribusi kekayaan dalam suatu populasi, karena sebagian besar disebabkan oleh sebagian kecil populasi. Namun saat ini Distribusi Pareto mempunyai banyak penerapan, misalnya dalam pengendalian kualitas, di bidang ekonomi, di bidang sains, di bidang sosial, dll.<\/p>\n<p> Nama distribusi Pareto diambil dari nama ekonom Vilfredo Pareto yang merumuskan distribusi tersebut. Namun, dia terkenal karena grafik Pareto. <\/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>Lihat:<\/strong> <a href=\"https:\/\/statorials.org\/id\/grafik-pareto\/\">Apa itu bagan Pareto?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-de-pareto\"><\/span> Tabel distribusi Pareto<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sekarang setelah kita mengetahui definisi distribusi Pareto, mari kita lihat beberapa contoh distribusi Pareto yang direpresentasikan secara grafis.<\/p>\n<p> Nah, di bawah ini Anda dapat melihat seperti apa grafik fungsi kepadatan distribusi Pareto tergantung pada nilai karakteristiknya: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/graphique-de-distribution-de-pareto.png\" alt=\"Bagan Distribusi Pareto\" class=\"wp-image-4774\" width=\"587\" height=\"413\" srcset=\"\" sizes=\"\"><\/figure>\n<p> Perhatikan bahwa domain distribusi Pareto berubah dari nilai x <sub>m<\/sub> menjadi +\u221e, itulah sebabnya fungsi kepadatan tidak ada sebelum nilai x <sub>m<\/sub> .<\/p>\n<p> Sedangkan grafik fungsi probabilitas kumulatif dari distribusi Pareto adalah sebagai berikut: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-de-probabilite-pareto-cumulative.png\" alt=\"probabilitas kumulatif dari distribusi Pareto\" class=\"wp-image-4775\" width=\"589\" height=\"414\" srcset=\"\" sizes=\"\"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-de-pareto\"><\/span> Ciri-ciri Distribusi Pareto<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Di bawah ini adalah karakteristik terpenting dari distribusi Pareto terkait teori probabilitas dan statistik.<\/p>\n<ul>\n<li> Distribusi Pareto mempunyai dua parameter karakteristik yang menentukan kurvanya: parameter skala x <sub>m<\/sub> dan parameter bentuk \u03b1.<\/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-c13a66a388e0a7e26781a0e8d9645f40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Pareto}(\\alpha,x_m)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Domain distribusi Pareto terdiri dari semua bilangan real dari parameter skala hingga plus tak terhingga.<\/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-c720ee182b49a794ed2862dd83a10ca9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in [x_m,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Jika \u03b1 lebih besar dari 1, rata-rata distribusi Pareto sama dengan hasil kali \u03b1 kali x <sub>m<\/sub> dan \u03b1 dikurangi 1.<\/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-6d26513868f9ed6fa45ab0fde0030884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{\\alpha\\cdot x_m}{\\alpha-1}\\quad\\text{para } \\alpha>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;34&#8243; width=&#8221;214&#8243; style=&#8221;vertical-align: -12px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Varians distribusi Pareto bergantung pada dua parameter karakteristik distribusi dan dihitung dengan 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-6120976b3586b76661d13bb9fdd5375d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Var(X)=\\frac{x_\\mathrm{m}^2\\cdot \\alpha}{(\\alpha-1)^2\\cdot(\\alpha-2)}\\quad \\text{para }\\alpha>2&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;44&#8243; width=&#8221;323&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Median distribusi Pareto dapat ditentukan dengan persamaan 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-0dc2c772a0a0662ad05f8b22c3cf1ba1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Me=x_\\mathrm{m}\\cdot \\sqrt[\\alpha]{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"113\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> Modus distribusi Pareto setara dengan parameter skala distribusi <sub>xm<\/sub> .<\/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-494f2f6e64851f90c504c989d93e22dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=x_m\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> Rumus fungsi kepadatan distribusi Pareto 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-1e182771cfe3bf9a145a2ee59b9c7eeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{\\alpha\\cdot x_m^\\alpha}{x^{\\alpha+1}}\\quad\\text{para }x\\geq x_m\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"262\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Demikian pula rumus fungsi probabilitas kumulatif dari distribusi Pareto 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-480adc7841b7c72cb4bfecb446ed3fab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=1-\\left(\\frac{x_\\mathrm{m}}{x}\\right)^\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"184\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Koefisien asimetri distribusi Pareto hanya bergantung pada parameter bentuk \u03b1 dan ekspresinya 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-98e7ba5f5d32988033c0f33d6af1bef8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\frac{2(1+\\alpha)}{\\alpha-3}\\,\\sqrt{\\frac{\\alpha-2}{\\alpha}}\\quad\\text{para }\\alpha>3&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;43&#8243; width=&#8221;274&#8243; style=&#8221;vertical-align: -14px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Koefisien kurtosis distribusi Pareto juga bervariasi tergantung pada nilai parameter \u03b1 dan dihitung 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-989019815fbeb266226cff9aa6b4a52b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\frac{6(\\alpha^3+\\alpha^2-6\\alpha-2)}{\\alpha(\\alpha-3)(\\alpha-4)}\\quad\\text{para }\\alpha>4&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;44&#8243; width=&#8221;299&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi Pareto dalam statistik dan kegunaannya. Anda juga akan dapat melihat grafik distribusi Pareto dan properti dari jenis distribusi probabilitas ini. Apa itu distribusi Pareto? Distribusi Pareto adalah distribusi probabilitas kontinu yang digunakan dalam statistik untuk memodelkan prinsip Pareto. Oleh karena itu, distribusi Pareto merupakan distribusi probabilitas yang memiliki beberapa [&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 pareto<\/title>\n<meta name=\"description\" content=\"Di sini Anda akan mempelajari apa itu Distribusi Pareto, kegunaannya, grafiknya, dan apa saja sifat-sifat Distribusi Pareto.\" \/>\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\/hukum-pareto\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Distribusi pareto\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan mempelajari apa itu Distribusi Pareto, kegunaannya, grafiknya, dan apa saja sifat-sifat Distribusi Pareto.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/hukum-pareto\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T21:54:17+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c13a66a388e0a7e26781a0e8d9645f40_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=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/hukum-pareto\/\",\"url\":\"https:\/\/statorials.org\/id\/hukum-pareto\/\",\"name\":\"\u25b7 Distribusi pareto\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-08-03T21:54:17+00:00\",\"dateModified\":\"2023-08-03T21:54:17+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Di sini Anda akan mempelajari apa itu Distribusi Pareto, kegunaannya, grafiknya, dan apa saja sifat-sifat Distribusi Pareto.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/hukum-pareto\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/hukum-pareto\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/hukum-pareto\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribusi pareto\"}]},{\"@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. 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