Horizontal Bimodal 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(24681012)

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 two well-separated normal components — the
// two clusters give each distribution its characteristic twin-hump shape.
function bimodal(n, a, b) {
  var out = []
  for (var i = 0; i < n; i++) {
    var c = rng() < a.w ? a : b
    out.push(Math.max(0, Math.round(gauss(c.mean, c.sd) * 10) / 10))
  }
  return out
}

// Session duration (minutes) per channel — a quick-bounce cluster and an
// engaged-visit cluster, mixed in different proportions.
var CHANNELS = [
  {
    name: 'Direct',
    data: bimodal(320, { w: 0.4, mean: 2, sd: 1 }, { mean: 22, sd: 5 }),
  },
  {
    name: 'Search',
    data: bimodal(320, { w: 0.55, mean: 2, sd: 1 }, { mean: 18, sd: 5 }),
  },
  {
    name: 'Social',
    data: bimodal(320, { w: 0.7, mean: 2, sd: 1 }, { mean: 14, sd: 4 }),
  },
  {
    name: 'Email',
    data: bimodal(320, { w: 0.3, mean: 3, sd: 1.5 }, { mean: 26, sd: 6 }),
  },
]

// Gaussian KDE with a loose bandwidth + coarse step, so the two humps stay
// distinct (a tighter bandwidth would smear them into one) and the outline
// keeps its angular, twin-peaked character.
function kde(values, bw, step) {
  var min = Math.min.apply(null, values) - bw
  var max = Math.max.apply(null, values) + bw
  var N = values.length
  var profile = []
  for (var x = min; x <= max; x += step) {
    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([Math.round(x * 100) / 100, sum / (N * bw)])
  }
  return profile
}

var options = {
  series: [
    {
      name: 'Sessions',
      data: CHANNELS.map(function (c) {
        return {
          x: c.name,
          y: { density: kde(c.data, 2.5, 1.5), points: c.data },
        }
      }),
    },
  ],
  chart: {
    type: 'violin',
    height: 480,
  },
  title: {
    text: 'Session duration by channel',
  },
  plotOptions: {
    bar: {
      horizontal: true,
      distributed: true,
    },
    violin: {
      normalize: 'group',
      points: { show: false }, // density curves only
    },
  },
  colors: ['#0ea5e9', '#F43F5E', '#f97316', '#10b981'],
  stroke: { width: 1, colors: ['#888'] },
  legend: { show: false },
  xaxis: {
    title: { text: 'Session duration (minutes)' },
  },
}

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