Distributor

Distributor at /distributor/ is a Jekyll page with native JavaScript modules. It uses the existing site build. Plotly draws the charts; jStat 1.9.6 supplies special functions, CDFs, and inverse CDFs. jStat is vendored in lib/ with its MIT license and an ES module wrapper. The old /distributions/ URL redirects here, preserving shared settings.

Add a distribution

Create one file in definitions/, then import it and add it to the array in registry.js. The dropdown and parameter controls are generated from that array.

For example, definitions/exponential.js could contain:

import { positive } from "../math.js";

export default {
  id: "exponential",
  name: "Exponential",
  description: "A positive distribution parameterized by rate.",
  parameters: [positive("rate", "λ", "Rate", 1, 0.1, 10)],
  support: () => [0, Infinity],
  logPdf: (x, { rate }) => x < 0 ? -Infinity : Math.log(rate) - rate * x,
  sample: ({ rate }, random) => -Math.log(random()) / rate,
  cdf: (x, { rate }) => x <= 0 ? 0 : -Math.expm1(-rate * x),
  quantile: (u, { rate }) => -Math.log1p(-u) / rate,
  moments: ({ rate }) => ({ mean: 1 / rate, sd: 1 / rate }),
};

Then add import exponential from "./definitions/exponential.js" and append exponential to distributions in registry.js.

The definition supplies:

• id, name, description, and parameters.
• logPdf(x, parameters) or pdf(x, parameters).
• sample(parameters, random), returning one draw using the supplied seeded generator.
• support(parameters), returning the lower and upper bounds; use Infinity for unbounded support.
• Optional cdf, quantile, mode, moments, and a TeX formula string. mode(parameters) returns a number or an array of modes, giving the plot an exact PDF peak.

quantile gives a deterministic default plot range and percentile summaries. Without it, the range comes from the sampled values. cdf supplies the probability-in-view readout. Missing statistics display a dash; use null for undefined moments and Infinity for divergent ones.

positive and real in math.js create parameter metadata. Suggested slider ranges are separate from mathematical bounds: typing a value outside the slider range expands it. Positive sliders use logarithmic steps. For custom metadata, see those helpers; a parameter needs key, symbol, label, default, and slider: { min, max, scale }.

Labels and sampling

Display labels never change mathematical parameter keys. Names and values are retained per distribution in the current tab’s session. Copy link includes the current distribution, labels, values, variable name, seed, and view. It takes no account or server storage.

Histograms use density normalization with the full sample size in the denominator, including draws outside the viewing window. Logarithmic bins use their widths in the original x units. Log x changes the axis scale; the density is still for X, not for log(X).

The y axis follows the theoretical PDF peak with 35% headroom, independent of the sampled bars. For singular boundary peaks, it uses finite interior density values. Fit range, the toolbar fit control, and double-clicking the plot all reset the view for the current parameters.

Development

From the repository root:

bundle exec jekyll serve --host 127.0.0.1 --port 4173
npm run test:distributions

Open http://127.0.0.1:4173/distributor/. Tests compare densities, CDFs, and quantiles against SciPy reference values, check sampler probabilities, and cover histogram normalization and saved settings. The site’s existing JavaScript minification script is independent of these modules.