2a:null 2b:["$","title",null,{"children":"Kumaraswamy distribution | Mattias Villani | Observable"}] 31:[] 2e:{"id":"b2776bb165853bef","slug":"kumaraswamy-distribution","title":"Kumaraswamy distribution","thumbnail":"306bda2805d02385ca4e075ce96c32fd9f2d3b52eed84c3f900bf7e9df6c1dc6","access_level":"public","create_time":"$D2023-05-28T19:23:56.769Z","update_time":"$D2023-10-03T12:59:35.074Z","view_time":null,"first_public_time":"$D2023-05-28T19:23:56.769Z","fork":{"id":"78f34b5c26815cb5","slug":"lognormal-distribution","title":"LogNormal distribution","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"stars":0,"starred":false,"owner":{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024"},"version":807,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null}],"members":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":3,"collection":{"id":"40c8ef5af1a51aff","slug":"distributions","title":"Statistical distributions","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"type":"notebook","body":{"title":"Kumaraswamy distribution","cells":[{"id":38,"value":"# Kumaraswamy distribution","pinned":false,"hidden":false,"mode":"md"},{"id":629,"value":"

${tex`X\\sim \\mathrm{Kumaraswamy}(a,b)`}","pinned":false,"hidden":false,"mode":"md"},{"id":496,"value":"The density function of a ${tex`X\\sim \\mathrm{Kumaraswamy}(a,b)`} random variable is\n\n${tex`f(x)=abx^{a-1}(1-x^a)^{b-1}\\text{ for } 0 d.x <= quantile, x: \"x\", y: \"pdf\", fill: \"purple\", opacity: 0.2})\n ]\n })","pinned":false,"hidden":false,"mode":"ojs"},{"id":109,"value":"
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\n\n---\n## 🙈 Appendix 🙈\n\nHere is some code and data details that you probably do not want to read.","pinned":false,"hidden":false,"mode":"md"},{"id":221,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md"},{"id":26,"value":"jstat = require('jstat')","pinned":false,"hidden":false,"mode":"ojs"},{"id":750,"value":"mathjs = require('mathjs')","pinned":true,"hidden":false,"mode":"ojs"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":654,"value":"a = params[0]","pinned":false,"hidden":false,"mode":"ojs"},{"id":656,"value":"b = params[1]","pinned":false,"hidden":false,"mode":"ojs"},{"id":662,"value":"quantile = params[2]","pinned":false,"hidden":false,"mode":"ojs"},{"id":706,"value":"mean = (b*mathjs.gamma(b)*mathjs.gamma(1+1/a))/mathjs.gamma(1+1/a+b)","pinned":false,"hidden":false,"mode":"ojs"},{"id":766,"value":"variance = b*jstat.betafn(1+2/a,b) - b**2*jstat.betafn(1+1/a,b)**2","pinned":false,"hidden":false,"mode":"ojs"},{"id":17,"value":"pdfdata = {\n const x = d3.range(0.00, 1, 0.001); \n const pdf = x.map(x => ({x: x, pdf: jstat.kumaraswamy.pdf(x, a, b )}));\n return pdf\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"cdf = jstat.kumaraswamy.cdf(quantile, a, b);","pinned":false,"hidden":false,"mode":"ojs"},{"id":229,"value":"#### Style","pinned":false,"hidden":false,"mode":"md"},{"id":202,"value":"","pinned":false,"hidden":false,"mode":"html"},{"id":58,"value":"viewof md_colour = Inputs.color({label: \"Highlight color cells\", value: \"#F5F5DC\"})","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}} 2f:"$2e:body"