F distribution

viewof params_f = Inputs.form([
      Inputs.range([1, 100], {value: 4, step: 1, label: tex`\nu_1`}),
      Inputs.range([1, 100], {value: 4, step: 1, label: tex`\nu_2`}),
      Inputs.range([0.01, 10], {value: 2, step: 0.01, label: "quantile:"})
    ])

dist_quantile_f = tex`\text{If } X \sim F(${nu1},${nu2}) \text{ then } `

moments_f = {
  if (nu2>4){
    return tex`
      \begin{aligned}
        &E( X) =\frac{\nu_2}{\nu_2-2} = ${(nu2/(nu2-2)).toPrecision(3)} \\[1em]
        &Var( X) = 2\Big(\frac{\nu_2}{\nu_2-2}\Big)^2\frac{\nu_1+\nu_2-2}{\nu_1(\nu_2-4)} = 
        ${(2*(nu2/(nu2-2))**2 * ((nu1+nu2-2)/(nu1*(nu2-4)))).toPrecision(3)} \\[1em]
        &P( X\leq ${quantile}) =${fcdf.toPrecision(4)}
      \end{aligned}
    `
  }
  else{
    if (nu2>2 && nu2<=4){
      return tex`
      \begin{aligned}
        &E( X) =\frac{\nu_2}{\nu_2-2} = ${(nu2/(nu2-2)).toPrecision(3)} ( \nu_2>2 \text{ is needed} )\\[1em]
        &Var( X) = \text{ does not exist} ( \nu_2>4 \text{ is needed} ) \\[1em]
        &P( X\leq ${quantile}) =${fcdf.toPrecision(4)}
      \end{aligned}
    `
    }
    else{
    return tex`
      \begin{aligned}
        &E( X) =\text{ does not exist} ( \nu_2>2 \text{ is needed} )\\[1em]
        &Var( X) = \text{ does not exist} ( \nu_2>4 \text{ is needed} ) \\[1em]
        &P( X\leq ${quantile}) =${fcdf.toPrecision(4)}
      \end{aligned}
    `
    }
  }
  
}

plt_pdf_f = 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(mode, nu1, nu2)]
    },
    marks: [
      Plot.ruleY([0]),
      Plot.ruleX([0]),
      Plot.line(fpdf, {x: "x", y: "pdf", stroke : "purple", strokeWidth: 2}),
      Plot.areaY(fpdf, {filter: d => d.x <= quantile, x: "x", y: "pdf", fill: "purple", opacity: 0.2})
    ]
  })

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

nu1 = params_f[0]
nu2 = params_f[1]
quantile = params_f[2]

fpdf = {
  const x = d3.range(0.01, jstat.centralF.inv( 0.99, nu1, nu2 ), 0.01);
  const pdf = x.map(x => ({x: x, pdf: jstat.centralF.pdf(x, nu1, nu2 )}));
  return pdf
}

fcdf = jstat.centralF.cdf(quantile, nu1, nu2);

jstat = require('jstat')