# statistics (engines/adapters/domain/statistics)

Inferential statistics capability pack (pure JavaScript, zero dependencies): descriptive summary (mean, median, mode, variance, standard deviation, min, max, range, quartiles, IQR, skewness...


Inferential-statistics capability pack. **Pure JavaScript, zero dependencies** — every special
function (erf / normal CDF, log-gamma, regularized incomplete beta & gamma for t / F / chi-square
p-values, Acklam inverse-normal) is implemented inline with Node built-ins only.

One contract (`export default { metadata, adapters }`); every tool takes ONE args object (an HTTP
POST body maps 1:1) and returns a plain JSON-serializable result. Numeric inputs are coerced from
JSON arrays, CSV/space strings, or single numbers; bad inputs throw `TypeError`/`Error`.

## Tools (17)

| tool | what it does |
|------|--------------|
| `describe` | full descriptive summary: mean, median, mode, min/max/range, Q1/Q3/IQR, sample & population variance/stdDev, skewness, excess kurtosis |
| `correlation` | Pearson (linear) or Spearman (rank) correlation of `x`,`y` + t-test significance (`method`) |
| `covariance` | sample (n-1) and population (n) covariance of `x`,`y` |
| `linearRegression` | ordinary least squares `y = slope·x + intercept`, R², std errors, slope t-test |
| `polynomialRegression` | least-squares polynomial fit of any `degree` (normal equations + Gaussian elimination), R² + adjusted R² |
| `tTest` | Student t-test: `one-sample` (vs `mu`), `two-sample` (Welch), or `paired` (`method`) |
| `zTest` | one-sample z-test with known population `sigma` |
| `chiSquareTest` | chi-square `goodness`-of-fit (`observed`/`expected`) or `independence` (2D contingency `observed`) |
| `anovaOneWay` | one-way ANOVA / F-test across `groups` (array of numeric arrays) |
| `confidenceInterval` | CI for a mean — t-interval (sigma unknown) or z-interval (`sigma` given), any `confidence` |
| `normalPdf` / `normalCdf` | normal density / cumulative probability at `value` for `mean`,`sigma` |
| `binomial` | binomial PMF `P(X=k)` or CDF (`cumulative`) for `n`,`p` |
| `poisson` | Poisson PMF `P(X=k)` or CDF (`cumulative`) for rate `lambda` |
| `zScore` | standardize one `value` (vs `mean`/`sigma`) or a whole `data` sample |
| `percentile` | value(s) at given `percentile`(s) via linear interpolation |
| `histogram` | equal-width bins (Sturges' rule default, or explicit `bins`) with counts + density |

## Usage

```js
import statistics from './index.js';

statistics.adapters.describe({ data: [4, 8, 15, 16, 23, 42] });
// { count: 6, mean: 18, median: 15.5, ... skewness, kurtosis }

statistics.adapters.tTest({ method: 'two-sample', x: [5, 7, 6, 8], y: [9, 11, 10, 12] });
// { variant: 'welch', t: ..., df: ..., pValue: ... }

statistics.adapters.linearRegression({ x: [1, 2, 3, 4], y: [2, 4, 6, 8] });
// { slope: 2, intercept: 0, rSquared: 1, equation: 'y = 2x + 0' }

statistics.adapters.binomial({ n: 10, p: 0.5, k: 3, cumulative: true });
```

`op` selects the tool when invoked through the adapter registry / MCP gateway. `adapterToServer()`
(`@leumas/mcp-kit`) exposes each tool as an MCP tool + HTTP endpoint + form.

## DRY boundary vs `numbers`

`numbers` owns **descriptive** series analytics (running average, normalize/scale, percentile
insights, anomaly detection, derivatives, weighted scoring) plus scalar math and unit/base
conversion. **This pack owns inferential statistics**: hypothesis tests, regression modelling,
correlation/covariance, probability distributions, confidence intervals, and
standardization/percentile/histogram utilities. `describe` is offered here as a fuller descriptive
summary (skew/kurtosis/quartiles) so a statistical workflow is self-contained — for lightweight,
streaming series work reach for `numbers` instead. Neither pack imports the other.


---
Source: shared/engines/adapters/domain/statistics/README.md
Canonical: https://docs.leumas.tech/p/adapters/domain/statistics