# Batch, Rolling, and Streaming Statistic Equivalence

`D00-F12-A04` · Financial Mathematics, Statistics, and Data Foundations → Statistical Computing and Reproducibility · archetype `record-transform` · difficulty 1/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/foundations/statistical-computing-and-reproducibility/batch-rolling-and-streaming-statistic-equivalence/
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 { batchRollingAndStreamingStatisticEquivalence } from "fintech-algorithms/foundations/statistical-computing-and-reproducibility/batch-rolling-and-streaming-statistic-equivalence";
```

## Signature

```ts
batchRollingAndStreamingStatisticEquivalence(input)
```

Computes the same fixed-window mean two ways, by re-averaging each window slice and by a running add-and-drop sum, then checks that they agree.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `D00Input` | yes | Reads `values`, a non-empty list of finite numbers, and `window`, the number of observations each average covers. |

## Returns

`D00Output`

`batchMean` averages the whole series. `rollingMeans` recomputes each window from its slice and `streamingMeans` maintains a running sum; `equivalent` is true when every matching pair agrees to within 1e-12.

## Errors

- When `values` is absent, empty, or holds a non-finite number — throws RangeError
- When `window` is not an integer between one and the observation count — throws RangeError

## Complexity

Time `O(n * w)`, 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, 3, 4, 5],
  "floatingValue": 0.1,
  "maxSafeMagnitude": 1.7976931348623157e+308,
  "window": 3,
  "rawValues": [1, null, 2, "bad", 3],
  "invalidPolicy": "drop-and-report",
  "seed": 42,
  "sampleCount": 5,
  "leftVector": [
    {
      "index": "A",
      "value": 1
    },
    {
      "index": "B",
      "value": 2
    }
  ],
  "rightVector": [
    {
      "index": "B",
      "value": 20
    },
    {
      "index": "C",
      "value": 30
    }
  ],
  "train": [10, 12, 14, 16],
  "test": [18, 20],
  "actual": [1, 2.0000001, 3],
  "expected": [1, 2, 3]
}
```

Showing 14 of 18 fields.

### Call

```ts
batchRollingAndStreamingStatisticEquivalence(input)
```

### Returns

object with 2 fields: batchMean, rollingMeans

```json
{
  "batchMean": 3,
  "rollingMeans": [2, 3, 4]
}
```

## 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/statistical-computing-and-reproducibility/batch-rolling-and-streaming-statistic-equivalence/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/statistical-computing-and-reproducibility/batch-rolling-and-streaming-statistic-equivalence/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt