# Uniform Distribution and Random Sampling

`D00-F07-A04` · Financial Mathematics, Statistics, and Data Foundations → Probability Distributions and Simulation Basics · archetype `record-transform` · difficulty 1/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/foundations/probability-distributions-and-simulation-basics/uniform-distribution-and-random-sampling/
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 { uniformDistributionAndRandomSampling } from "fintech-algorithms/foundations/probability-distributions-and-simulation-basics/uniform-distribution-and-random-sampling";
```

## Signature

```ts
uniformDistributionAndRandomSampling(input)
```

Draws `sampleCount` values on the unit interval from a seeded linear congruential generator and reports the draws with their support and realised mean.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `D00Input` | yes | One record carrying `seed` (the generator's starting state) and `sampleCount` (how many draws to produce), plus `p`, which the family entry point validates before dispatching. · sampleCount: 1 or greater, p: between 0 and 1 inclusive |

## Returns

`D00Output`

An object with `samples` (the draws, each in the half-open unit interval), `minimum` and `maximum` (the theoretical support, always 0 and 1) and `sampleMean` (the mean of the draws actually produced).

## Errors

- When p is missing or outside 0 to 1 — this check runs for every topic in the family — throws RangeError
- When sampleCount is below 1 — throws RangeError

## Complexity

Time `O(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": [0.2, 0.5, 0.7, 1, 1.4],
  "x": 1,
  "p": 0.3,
  "n": 5,
  "k": 2,
  "lambda": 2,
  "seed": 42,
  "sampleCount": 8,
  "mu": 0,
  "sigma": 1,
  "df": 5,
  "shape": 2,
  "scale": 1.5,
  "components": [
    {
      "weight": 0.7,
      "mean": 0,
      "sd": 1
    },
    {
      "weight": 0.3,
      "mean": 3,
      "sd": 0.8
    }
  ]
}
```

### Call

```ts
uniformDistributionAndRandomSampling(input)
```

### Returns

object with 2 fields: samples, minimum

```json
{
  "samples": [
    0.2523451747838408,
    0.08812504541128874,
    0.5772811982315034,
    0.22255426598712802,
    0.37566019711084664,
    0.02566390484571457
  ],
  "minimum": 0
}
```

## 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/probability-distributions-and-simulation-basics/uniform-distribution-and-random-sampling/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/probability-distributions-and-simulation-basics/uniform-distribution-and-random-sampling/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt