2b:null 2c:["$","title",null,{"children":"Triangular distribution | Mattias Villani | Observable"}] 31:[] 2f:{"id":"1966acea1bb69560","slug":"triangular-distribution","title":"Triangular distribution","thumbnail":"84374ef7ad2a490c57ce6a9d13ba1425b9e29428242145b77f7b09db5a26f7f5","access_level":"public","create_time":"$D2023-04-27T11:28:45.391Z","update_time":"$D2023-09-04T09:20:20.612Z","view_time":null,"first_public_time":"$D2023-04-27T11:28:45.391Z","fork":{"id":"882386ab35e15d86","slug":"weibull-distribution","title":"Weibull 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":806,"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":1,"collection":{"id":"40c8ef5af1a51aff","slug":"distributions","title":"Statistical distributions","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"type":"notebook","body":{"title":"Triangular distribution","cells":[{"id":38,"value":"# Triangular distribution","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":629,"value":"

${tex`X\\sim \\mathrm{Triangular}(a,b,c)`}, for ${tex`a\\leq X \\leq b`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":496,"value":"## Probability density function and moments","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":767,"value":"viewof params = Inputs.form([\n Inputs.range([-5, 5], {value: 0, step: 0.1, label: tex`\\text{lower, }a`}),\n Inputs.range([-5, 5], {value: 1, step: 0.1, label: tex`\\text{upper, }b`}),\n Inputs.range([-5, 5], {value: 0.5, step: 0.1, label: tex`\\text{mode, }c`}),\n Inputs.range([-5, 5], {value: 1, step: 0.1, label: \"quantile:\"})\n ])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":461,"value":"dist_quantile = tex`\\text{If } X \\sim \\mathrm{Triangular}(${a.toPrecision(2)},${b.toPrecision(2)},${c.toPrecision(2)}) \\text{ then } `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":555,"value":"moments = {\n\n if (a d.x <= quantile, x: \"x\", y: \"pdf\", fill: \"orange\", opacity: 0.2})\n ]\n })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"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","author":"$undefined","summary":"$undefined"},{"id":221,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":26,"value":"jstat = require('jstat')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":746,"value":"mathjs = require('mathjs')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":654,"value":"a = params[0]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":656,"value":"b= params[1]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":778,"value":"c = params[2]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":662,"value":"quantile = params[3]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":706,"value":"mean = (a+b+c)/3","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":709,"value":"variance = (a**2 + b**2 + c**2 - a*b - a*c - b*c)/(18)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":17,"value":"pdf = {\n const x = d3.range(-5, 5, 0.01); // use jstat.lognormal.inv( 0.999, mu, sigma ) as upper if needed\n const pdf = x.map(x => ({x: x, pdf: jstat.triangular.pdf(x, a, b, c )}));\n return pdf\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":19,"value":"cdf = jstat.triangular.cdf(quantile, a, b, c);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":229,"value":"#### Style","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":202,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined"},{"id":58,"value":"viewof md_colour = Inputs.color({label: \"Highlight color cells\", value: \"#F5F5DC\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"