Chi-squared distribution

viewof params = Inputs.form([
      Inputs.range([1, 100], {value: 4, step: 1, label: tex`\nu`}),
      Inputs.range([0.01, 50], {value: 2, step: 0.01, label: "quantile:"})
    ])

dist_quantile = tex`\text{If } X \sim \chi^2_{${params[0]}} \text{ then } \\[1em]`

moments = tex`
\begin{aligned}
&E( X) =\nu = ${params[0].toPrecision(3)} \\[1em]
&Var( X) =2\nu= ${(2*params[0]).toPrecision(3)} \\[1em]
&P( X\leq ${params[1]}) =${chisquarecdf.toPrecision(4)}
\end{aligned}
`

plt_pdf = Plot.plot({
    width: 800, // or a dynamic value based on `width` variable
    height: 600,
    style: {fontSize: "15px"},
    color: {
      legend: true
    },
    x: {
      label: "x",
      axis: true
    },
    y: {
      label: "f(x)",
      //axis: false,
      domain: [0,jstat.chisquare.pdf(Math.max(0,params[0]-2), params[0])]
    },
    marks: [
      Plot.ruleY([0]),
      Plot.ruleX([0]),
      Plot.line(chisquarepdf, {x: "x", y: "pdf", stroke : "steelblue", strokeWidth: 2}),
      Plot.areaY(chisquarepdf, {filter: d => d.x <= params[1], x: "x", y: "pdf", fill: "steelblue", opacity: 0.2})
    ]
  })

Figure 1: https://observablehq.com/@mattiasvillani/chi2-distribution

chisquarepdf = {
  const x = d3.range(0.01, params[0]+5*Math.sqrt(2*params[0]), 0.01);
  const pdf = x.map(x => ({x: x, pdf: jstat.chisquare.pdf(x, params[0])}));
  return pdf
}

chisquarecdf = jstat.chisquare.cdf(params[1], params[0]);

jstat = require('jstat')