2a:null 2b:["$","title",null,{"children":"Intro to Observable notebooks | Mattias Villani | Observable"}] 31:[{"id":"e6de228b1e681297bf0651952f0da700505ceb2a6d2b155f4a01eb88ea9b2335cdbc193afc3a21c0f686310781827ce028bf022466c9087359f9097f94870538","href":"https://static.observableusercontent.com/files/e6de228b1e681297bf0651952f0da700505ceb2a6d2b155f4a01eb88ea9b2335cdbc193afc3a21c0f686310781827ce028bf022466c9087359f9097f94870538","name":"girl1.png","type":"image/png","lastModified":1740060388048.868,"size":94337},{"id":"96d22a33e0d89f7e949047736e46d8cec8d215b16a8f788722dc7286c00f0e6c00e73bee497f67f7a265e408f501b0e0682613579fe104175f03251ec9f18937","href":"https://static.observableusercontent.com/files/96d22a33e0d89f7e949047736e46d8cec8d215b16a8f788722dc7286c00f0e6c00e73bee497f67f7a265e408f501b0e0682613579fe104175f03251ec9f18937","name":"girl2.png","type":"image/png","lastModified":1740060398225.439,"size":71919},{"id":"891b00cee9bc7de671e7c975f28cbe78f87189b6e3dd32ee5ca09043175958d28a8926fad1020784c8952237d364548f4915880fe754b78d8328575a249460aa","href":"https://static.observableusercontent.com/files/891b00cee9bc7de671e7c975f28cbe78f87189b6e3dd32ee5ca09043175958d28a8926fad1020784c8952237d364548f4915880fe754b78d8328575a249460aa","name":"palmer-penguins.csv","type":"text/csv","lastModified":1740061051151.636,"size":19263}] 2e:{"id":"b30596b30bbd232c","slug":"intro-to-observable","title":"Intro to Observable notebooks","thumbnail":"6a951f7352d300d25475668f918519cd19f3e78ecb8cae5e18c9bb3020aa317c","access_level":"public","create_time":"$D2025-02-20T13:59:01.099Z","update_time":"$D2025-02-20T15:59:44.640Z","view_time":null,"first_public_time":"$D2025-02-20T13:59:01.099Z","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":906,"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"},{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Intro to Observable notebooks","cells":[{"id":38,"value":"# Intro to Observable notebooks","pinned":false,"hidden":false,"mode":"md"},{"id":809,"value":"### Markdown \nThe [usual stuff](https://www.markdownguide.org/cheat-sheet/) works: *italic*, **bold**.\n\nBulleted list:\n- first item\n- second item\n\nor numbered\n\n1. first\n2. second\n3. third","pinned":false,"hidden":false,"mode":"md"},{"id":828,"value":"

HTML cells

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Hej mor

","pinned":false,"hidden":false,"mode":"html"},{"id":843,"value":"LaTeX math is support either inline ${tex`\\alpha = \\frac{1}{(1-p)}`} (just kidding: ${tex`\\alpha = \\frac{1}{1-p}`}) or in display mode\n${tex.block`y = \\beta_0 + \\beta_1 x + \\varepsilon`}","pinned":false,"hidden":false,"mode":"md"},{"id":849,"value":"Files can uploaded at attachment, for example data:\n","pinned":false,"hidden":false,"mode":"md"},{"id":852,"value":"penguinsData = FileAttachment(\"palmer-penguins.csv\").csv({typed: true});","pinned":false,"hidden":false,"mode":"ojs"},{"id":855,"value":"viewof table = Inputs.table(penguinsData)","pinned":false,"hidden":false,"mode":"ojs"},{"id":859,"value":"or images:","pinned":false,"hidden":false,"mode":"md"},{"id":823,"value":"girl2 = FileAttachment(\"girl2.png\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":877,"value":"### Interactive elements","pinned":false,"hidden":false,"mode":"md"},{"id":869,"value":"The value from a slider is attached to a variable with the Observable-specific `viewof` command:","pinned":false,"hidden":false,"mode":"md"},{"id":867,"value":"viewof weight = Inputs.range([0, 120], {label: \"Weight\", step: 1, value: 84})","pinned":false,"hidden":false,"mode":"ojs"},{"id":879,"value":"My weight is: ${weight}","pinned":false,"hidden":false,"mode":"md"},{"id":874,"value":"viewof checkboxes = Inputs.checkbox([\"A\", \"B\", \"C\"], {label: \"Select some\", value: [\"A\", \"B\"]})","pinned":false,"hidden":false,"mode":"ojs"},{"id":903,"value":"viewof range = Inputs.range([0, 100], {label: \"Amount\", step: 1})","pinned":true,"hidden":false,"mode":"ojs"},{"id":905,"value":"viewof checkboxes1 = Inputs.checkbox([\"A\", \"B\"], {label: \"Select some\", value: [\"A\"]})","pinned":true,"hidden":false,"mode":"ojs"},{"id":862,"value":"Here follows the an implementation of the Weibull distribution.","pinned":false,"hidden":false,"mode":"md"},{"id":770,"value":"The density function of a ${tex`X \\sim \\mathrm{Weibull}(\\lambda,k)`} random variable is \n\n${tex`f(x)=\\frac{k}{\\lambda}\\left(\\frac{x}{\\lambda}\\right)^{k-1}e^{-(x/\\lambda)^k}`} for ${tex`x>0`}","pinned":false,"hidden":false,"mode":"md"},{"id":118,"value":"viewof params = Inputs.form([\n Inputs.range([0.0, 10], {value: 1, step: 0.1, label: tex`\\lambda`}),\n Inputs.range([0.0, 10], {value: 1, step: 0.1, label: tex`k`}),\n Inputs.range([0, 10], {value: 1, step: 0.1, label: \"quantile:\"})\n ])","pinned":false,"hidden":false,"mode":"ojs"},{"id":461,"value":"dist_quantile = tex`\\text{If } X \\sim \\mathrm{Weibull}(${lambda},${(k).toPrecision(2)}^2) \\text{ then } `","pinned":false,"hidden":false,"mode":"ojs"},{"id":555,"value":"moments = {\n \n return tex`\n \\begin{aligned}\n &E( X) = \\lambda \\Gamma\\Big(1+\\frac{1}{k}\\Big) = ${(mean).toPrecision(3)} \\\\[1em]\n &Var( X) = \\lambda^2 \\left(\\Gamma\\left(1+\\frac{2}{k}\\right) - \\Gamma\\left(1+\\frac{1}{k}\\right)^2\\right) = ${(variance).toPrecision(3)} \\\\[1em]\n &P( X\\leq ${quantile}) =${cdf.toPrecision(4)}\n \\end{aligned}\n `\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":305,"value":"plt_pdf = Plot.plot({\n color: {\n legend: true\n },\n title: \"Weibull density\",\n x: {\n label: \"x\",\n axis: true\n },\n y: {\n label: \"f(x)\"\n },\n marks: [\n Plot.ruleY([0]),\n Plot.ruleX([0]),\n Plot.line(pdf, {x: \"x\", y: \"pdf\", stroke : \"green\", strokeWidth: 2}),\n Plot.areaY(pdf, {filter: d => d.x <= quantile, x: \"x\", y: \"pdf\", fill: \"green\", 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":746,"value":"mathjs = require('mathjs')","pinned":false,"hidden":false,"mode":"ojs"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":654,"value":"lambda = params[0]","pinned":false,"hidden":false,"mode":"ojs"},{"id":656,"value":"k = params[1]","pinned":false,"hidden":false,"mode":"ojs"},{"id":662,"value":"quantile = params[2]","pinned":false,"hidden":false,"mode":"ojs"},{"id":706,"value":"mean = lambda*mathjs.gamma(1 + 1/k)","pinned":false,"hidden":false,"mode":"ojs"},{"id":709,"value":"variance = lambda**2*( mathjs.gamma(1 + 2/k) - mathjs.gamma(1+ 1/k)**2 )","pinned":false,"hidden":false,"mode":"ojs"},{"id":17,"value":"pdf = {\n const x = d3.range(0.01, 10, 0.01); // use jstat.lognormal.inv( 0.999, mu, sigma ) as upper if needed\n const pdf = x.map(x => ({x: x, pdf: jstat.weibull.pdf(x, lambda, k )}));\n return pdf\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"cdf = jstat.weibull.cdf(quantile, lambda, k);","pinned":false,"hidden":false,"mode":"ojs"},{"id":885,"value":"### Own implementation of the Weibull CDF","pinned":false,"hidden":false,"mode":"md"},{"id":883,"value":"function mycdf(x){\n const cdfValue = 1 - Math.exp(-((x/lambda)**k))\n return cdfValue\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":888,"value":"mycdf(quantile)","pinned":false,"hidden":false,"mode":"ojs"},{"id":229,"value":"#### Style","pinned":false,"hidden":false,"mode":"md"}],"files":"$W31","stdlib":"1","titling":"auto"}} 2f:"$2e:body"