Violin with Jitter in JavaScript

// ── Reproducible synthetic data (seeded PRNG, no network) ──────────────
function mulberry32(a) {
  return function () {
    a |= 0
    a = (a + 0x6d2b79f5) | 0
    var t = Math.imul(a ^ (a >>> 15), 1 | a)
    t = (t + Math.imul(t ^ (t >>> 7), 61 | t)) ^ t
    return ((t ^ (t >>> 14)) >>> 0) / 4294967296
  }
}
var rng = mulberry32(20240607)

function gauss(mean, sd) {
  var u = 0,
    v = 0
  while (u === 0) u = rng()
  while (v === 0) v = rng()
  return mean + sd * Math.sqrt(-2 * Math.log(u)) * Math.cos(2 * Math.PI * v)
}

// Draw n samples from a mixture of normal components — the mixture is what
// gives each violin its characteristic multi-modal (lumpy) shape.
function mixture(n, comps) {
  var out = []
  for (var i = 0; i < n; i++) {
    var r = rng(),
      acc = 0,
      c = comps[0]
    for (var k = 0; k < comps.length; k++) {
      acc += comps[k].w
      if (r <= acc) {
        c = comps[k]
        break
      }
    }
    out.push(Math.max(5, Math.round(gauss(c.mean, c.sd) * 10) / 10))
  }
  return out
}

// Daily commute time (minutes) — each city mixes a couple of "transport
// mode" clusters (e.g. metro vs. road) for a realistic bimodal spread.
var CITIES = [
  {
    name: 'Tokyo',
    data: mixture(260, [
      { w: 0.62, mean: 42, sd: 5 },
      { w: 0.38, mean: 58, sd: 5 },
    ]),
  },
  {
    name: 'London',
    data: mixture(260, [
      { w: 0.7, mean: 48, sd: 7 },
      { w: 0.3, mean: 74, sd: 6 },
    ]),
  },
  {
    name: 'New York',
    data: mixture(260, [{ w: 1, mean: 50, sd: 11 }]),
  },
  {
    name: 'Berlin',
    data: mixture(260, [
      { w: 0.8, mean: 37, sd: 5 },
      { w: 0.2, mean: 54, sd: 5 },
    ]),
  },
]

// ── Gaussian KDE (bandwidth controls smoothness) ───────────────────────
function kde(values, bw) {
  var min = Math.min.apply(null, values)
  var max = Math.max.apply(null, values)
  var N = values.length
  var profile = []
  // Keep the tail short (1 bandwidth) so the violin tapers cleanly without
  // a long near-zero spike that would drag the axis toward 0.
  for (var x = min - bw; x <= max + bw; x += 1) {
    var sum = 0
    for (var k = 0; k < N; k++) {
      var d = (x - values[k]) / bw
      sum += Math.exp(-0.5 * d * d)
    }
    profile.push([x, sum / (N * bw)])
  }
  return profile
}

function quantile(sorted, q) {
  var pos = (sorted.length - 1) * q
  var b = Math.floor(pos)
  var r = pos - b
  return sorted[b + 1] !== undefined
    ? sorted[b] + r * (sorted[b + 1] - sorted[b])
    : sorted[b]
}
function fiveNum(values) {
  var s = values.slice().sort(function (a, b) {
    return a - b
  })
  return {
    min: s[0],
    q1: quantile(s, 0.25),
    median: quantile(s, 0.5),
    q3: quantile(s, 0.75),
    max: s[s.length - 1],
  }
}

var BW = 2.5
var LABELS = CITIES.map(function (c) {
  return c.name
})
var COLORS = ['#14b8a6', '#3B82F6', '#f59e0b', '#ef4444'] // teal, blue, amber, red
var stats = CITIES.map(function (c) {
  return fiveNum(c.data)
})

var options = {
  series: [
    {
      name: 'Commute',
      data: CITIES.map(function (c) {
        return {
          x: c.name,
          y: { density: kde(c.data, BW), points: c.data },
        }
      }),
    },
  ],
  chart: {
    type: 'violin',
    height: 560,
  },
  title: {
    text: 'Daily commute time by city',
    align: 'center',
  },
  colors: COLORS,
  plotOptions: {
    bar: { distributed: true }, // one colour per city
    violin: {
      normalize: 'group', // widths track density across cities
      // dots in a darker shade of each violin's colour, with a white outline
      points: { show: true, size: 3, jitter: 0.6 },
    },
  },
  stroke: { width: 1, colors: ['#888'] },
  legend: { show: false },
  yaxis: {
    labels: {
      formatter: function (v) {
        return Math.round(v) + ' min'
      },
    },
  },
  tooltip: {
    shared: false,
    custom: function (o) {
      var st = stats[o.dataPointIndex]
      if (!st) return ''
      var row = function (label, val) {
        return (
          '<tr><td style="padding:2px 8px">' +
          label +
          ':</td><td style="padding:2px 8px"><b>' +
          val.toFixed(1) +
          ' min</b></td></tr>'
        )
      }
      return (
        '<div class="apexcharts-tooltip-box" style="padding:6px">' +
        '<div style="font-weight:600;margin-bottom:2px">' +
        LABELS[o.dataPointIndex] +
        '</div><table>' +
        row('Max', st.max) +
        row('Q3', st.q3) +
        row('Median', st.median) +
        row('Q1', st.q1) +
        row('Min', st.min) +
        '</table></div>'
      )
    },
  },
}

var chart = new ApexCharts(document.querySelector('#chart'), options)
chart.render()