# Histograms and Empirical Distribution Functions

`D00-F04-A09` · Financial Mathematics, Statistics, and Data Foundations → Location, Ranking, and Exploratory Summaries · archetype `record-transform` · difficulty 1/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

```ts
import { histogramsAndEmpiricalDistributionFunctions } from "fintech-algorithms/foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions";
```

## Signature

```ts
histogramsAndEmpiricalDistributionFunctions(input)
```

Splits the observed span into equal-width bins and counts the observations in each, alongside the empirical distribution function evaluated at every sorted observation.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `{ values: number[]; bins: number }` | yes | `values` holds the observations and `bins` the number of equal-width buckets to spread them across. The bins span minimum to maximum; when every observation is identical the width falls back to 1 and everything lands in the last bin. · bins: integer, at least 1 |

## Returns

`{ binCounts: number[]; binWidth: number; ecdf: { x: number; p: number }[] }`

`binCounts` has one entry per bin in ascending order, `binWidth` is the common width used, and `ecdf` pairs each sorted observation `x` with the cumulative share `p` of observations at or below its position.

## Errors

- When `input` is null, an array, or not an object — throws TypeError
- When `values` is missing, is not an array, or is empty — throws RangeError
- When any entry of `values` does not coerce to a finite number — throws RangeError
- When `bins` is not an integer or is less than 1 — throws RangeError

## Complexity

Time `O(n log n)`, space `O(n)`.

## Worked example

This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

### Input

`input`:

```json
{
  "values": [1, 2, 2, 4, 9],
  "weights": [1, 1, 2, 1, 1],
  "trimProportion": 0.2,
  "bins": 4
}
```

### Call

```ts
histogramsAndEmpiricalDistributionFunctions(input)
```

### Returns

object with 2 fields: binCounts, binWidth

```json
{
  "binCounts": [3, 1, 0, 1],
  "binWidth": 2
}
```

## Verification and provenance

Tier: **verified** (via input-expected).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.0.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/location-ranking-and-exploratory-summaries/histograms-and-empirical-distribution-functions/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt