31:[] 2f:{"title":"Hypergeometric distribution","cells":[{"id":38,"value":"# Hypergeometric distribution","pinned":false,"hidden":false,"mode":"md"},{"id":780,"value":"disttext = md`

${tex`X\\sim \\operatorname{HyperGeo}(N,K,n)`}, for ${tex`X \\in \\{\\max(0,n+K-N),\\ldots,\\min(n,K) \\}`}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":496,"value":"## Probability mass function and moments","pinned":false,"hidden":false,"mode":"md"},{"id":118,"value":"viewof N = Inputs.range([0, 1000], {value: 500, step: 1, label: tex`\\text{pop size } N`})","pinned":false,"hidden":false,"mode":"ojs"},{"id":799,"value":"viewof K = Inputs.range([0, N], {value: 50, step: 1, label: tex`\\text{no. success items }K`})","pinned":false,"hidden":false,"mode":"ojs"},{"id":807,"value":"viewof n = Inputs.range([0, N], {value: 100, step: 1, label: tex`\\text{sample size }n`})","pinned":false,"hidden":false,"mode":"ojs"},{"id":803,"value":"viewof quantile = Inputs.range([d3.max([0,n+K-N]), d3.min([n,K])], {value: 7, step: 1, label: \"Quantile:\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":461,"value":"dist_quantile = tex`\\text{If } X \\sim \\operatorname{HyperGeo}(N=${N},K=${K},n=${n}) \\text{ then } `","pinned":false,"hidden":false,"mode":"ojs"},{"id":555,"value":"moments = tex`\n\\begin{aligned}\n&E( X) = \\lambda = ${mean.toPrecision(3)} \\\\[1em]\n&Var( X) = \\lambda = ${variance.toPrecision(3)} \\\\[1em]\n&P( X\\leq ${quantile}) =${hypergeocdf.toPrecision(4)}\n\\end{aligned}\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":305,"value":"plt_pdf = Plot.plot({\n color: { \n legend: false\n },\n x: {\n label: \"x\",\n axis: true,\n ticks: xTicks,\n },\n y: {\n label: \"f(x)\",\n axis: true\n },\n tooltip: {\n fill: \"gray\",\n stroke: \"gray\",\n opacity: 1,\n },\n marks: [\n Plot.ruleY([0]),\n Plot.barY(hypergeopdf,{x: \"x\", y: \"pdf\", fill: \"pink\", strokeWidth: 0, opacity: 1,\n title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`}),\n Plot.barY(hypergeopdf, {filter: d => d.x <= quantile, x: \"x\", y: \"pdf\", fill: \"purple\", opacity: 1,\n title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`}),\n ]\n })","pinned":false,"hidden":false,"mode":"ojs"},{"id":109,"value":"
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\n\n---\n## 🙈 Appendix 🙈\n\nJust some code and details that you probably do not want to read.","pinned":false,"hidden":false,"mode":"md"},{"id":221,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md"},{"id":26,"value":"jstat = require('jstat')","pinned":false,"hidden":false,"mode":"ojs"},{"id":764,"value":"import {Plot} from \"@mkfreeman/plot-tooltip\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":840,"value":"mean = (n*K/N)","pinned":true,"hidden":false,"mode":"ojs"},{"id":843,"value":"variance = ((n*K/N)*((N-K)/N)*((N-n)/(N-1)))","pinned":false,"hidden":false,"mode":"ojs"},{"id":17,"value":"hypergeopdf = { \n const x = d3.range(d3.max([0,n+K-N]), Math.ceil(mean + 5*Math.sqrt(variance)), 1)\n const data = x.map(x => ({x: x, pdf: jstat.hypgeom.pdf(x, N, K, n)}));\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"hypergeocdf = jstat.hypgeom.cdf(quantile, N, K, n);","pinned":false,"hidden":false,"mode":"ojs"},{"id":895,"value":"xTicks = {\n if(mean<20){\n return d3.range(d3.max([0,n+K-N]), Math.ceil(mean + 5*Math.sqrt(variance)), 1)}\n else{return d3.range(d3.max([0,n+K-N]), Math.ceil(mean + 5*Math.sqrt(variance)), 5)}\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":229,"value":"#### Style","pinned":false,"hidden":false,"mode":"md"},{"id":202,"value":"","pinned":false,"hidden":false,"mode":"html"},{"id":58,"value":"viewof md_colour = Inputs.color({label: \"Highlight color cells\", value: \"#F5F5DC\"})","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}