2b:null 2c:["$","title",null,{"children":"Geometric distribution | Mattias Villani | Observable"}] 31:[] 2f:{"id":"8a7e6032ab432031","slug":"geometric-distribution","title":"Geometric distribution","thumbnail":"f0c5c3b2791898e91ed4ab0325c6e22c4f5d2d728c35d3bd7989d46cec9d8c78","access_level":"public","create_time":"$D2023-02-25T15:23:41.566Z","update_time":"$D2023-09-04T15:33:23.350Z","view_time":null,"first_public_time":"$D2023-02-25T15:23:41.566Z","fork":{"id":"15db2285aae0bfdd","slug":"geometrisk-fordelning","title":"Geometrisk fördelning","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":795,"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":"Geometric distribution","cells":[{"id":38,"value":"# Geometric distribution","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":776,"value":"

${tex`X\\sim \\operatorname{Geom}(p)`}, for ${tex`X \\in \\{0,1,2,\\ldots\\}`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":496,"value":"## Probability mass function and moments","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":118,"value":"viewof params = Inputs.form([\n Inputs.range([0, 1], {value: 0.5, step: 0.01, label: tex`p:`}),\n Inputs.range([0, 10], {value: 3, step: 1, label: \"quantile:\"})\n ])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":461,"value":"dist_quantile = tex`\\text{If } X \\sim \\operatorname{Geom}(${params[0]}) \\text{ then } `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":555,"value":"moments = tex`\n\\begin{aligned}\n&E( X) = \\frac{1-p}{p} = ${((1-params[0])/params[0]).toPrecision(3)} \\\\[1em]\n&Var( X) = \\frac{1-p}{p^2} =${((1-params[0])/(params[0]^2)).toPrecision(3)} \\\\[1em]\n&P( X\\leq ${params[1]}) =${geomcdf.toPrecision(4)}\n\\end{aligned}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":305,"value":"plt_pdf = Plot.plot({\n color: { \n legend: false\n },\n x: {\n label: \"x\",\n axis: true\n },\n y: {\n label: \"f(x)\",\n axis: true\n },\n tooltip: {\n fill: \"#0F52BA\",\n stroke: \"#0F52BA\",\n opacity: 1,\n },\n marks: [\n Plot.ruleY([0]),\n Plot.barY(geompdf,{x: \"x\", y: \"pdf\", fill: \"#B6D0E2\", strokeWidth: 0, opacity: 1,\n title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`}),\n Plot.barY(geompdf, {filter: d => d.x <= params[1], x: \"x\", y: \"pdf\", fill: \"#6F8FAF\", opacity: 1,\n title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`})\n ]\n })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":109,"value":"
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\n\n---\n## 🙈 Appendix 🙈\n\nJust some code and details below.","pinned":false,"hidden":false,"mode":"md","author":"$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":"$undefined"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":17,"value":"geompdf = {\n const p = params[0];\n const x = d3.range(0, ((1-p)/p) + 3*Math.sqrt(((1-p)/p**2)), 1);\n const data = x.map(x => ({x: x, pdf: jstat.negbin.pdf(x, 1, params[0])}));\n return data\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":19,"value":"geomcdf = jstat.negbin.cdf(params[1], 1, params[0]);","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":740,"value":"import {Plot} from \"@mkfreeman/plot-tooltip\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"