Poisson Distribution

jstat = require('jstat')

viewof params_pois = Inputs.form([
      Inputs.range([0.1, 20], {value: 2, step: 0.1, label: tex`\lambda:`}),
      Inputs.range([1, 40], {value: 1, step: 1, label: "quantile:"})
    ])

dist_quantile_pois = tex`\text{If } X \sim \operatorname{Poisson}(${params_pois[0]}) \text{ then } `

moments_pois = tex`
\begin{aligned}
&\mathrm{E}( X) =  \lambda = ${params_pois[0].toPrecision(3)} \\[0.5em]
&\mathrm{Var}( X) =  \lambda  = ${params_pois[0].toPrecision(3)} \\[0.5em]
&\mathrm{P}( X\leq ${params_pois[1]}) =${poiscdf.toPrecision(4)}
\end{aligned}
`

plt_pois = Plot.plot({
    width: 700, // or a dynamic value based on `width` variable
    height: 400,
    color: {
      legend: false
    },
    x: {
      label: "x",
      axis: true,
      labelOffset: 30
    },
    y: {
      label: "P(X = x)",
      axis: true
    },
   style: {
    fontSize: 16,         // overall font size (tick labels + titles)
    fontFamily: "sans-serif"
    },
  tooltip: {
    fill: "#097969",
    stroke: "#097969",
    opacity: 1,
  },
    marks: [
      Plot.ruleY([0]),
      Plot.barY(poispdf,{x: "x", y: "pdf", fill: "#C1E1C1", strokeWidth: 0, opacity: 1,
                title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`}),
      Plot.barY(poispdf, {filter: d => d.x <= params_pois[1], x: "x", y: "pdf", fill: "#50C878", opacity: 1,
                title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`})
    ]
  })

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

poispdf = {
  const x = d3.range(0, params_pois[0] + 4*Math.sqrt(params_pois[0]), 1);
  const data = x.map(x => ({x: x, pdf: jstat.poisson.pdf(x, params_pois[0])}));
  return data
}

poiscdf = jstat.poisson.cdf(params_pois[1], params_pois[0]);