Central Limit Theorem

Install and import#

bash

npm install fintech-algorithms

import { centralLimitTheorem } from "fintech-algorithms/foundations/sampling-estimation-and-statistical-inference/central-limit-theorem";

Signature#

centralLimitTheorem(input)

Standardises the replicated estimates in input.estimates by subtracting populationMean and dividing by their spread, then checks how close the standardised values sit to zero.

Parameters#

Name	Type	Notes
`input`	`D00Input`	One record. `estimates` holds one sample mean per replication and `populationMean` is the value they are centred on. `sample` and `alpha` are validated for the whole family before dispatch. sample: non-empty list of finite numbers, at least two of them · estimates: non-empty list of finite numbers · alpha: strictly between 0 and 1

Returns#

D00Output

An object with standardizedMeans (one per replication), center (their mean) and approximatelyCentered (true when center is within 0.5 of zero).

Errors#

When sample or estimates is missing, empty, or contains a non-finite number — both are parsed for every topic in the family, whether or not the topic uses them — throws RangeError
When sample holds fewer than two observations — throws RangeError
When alpha is not strictly between zero and one — throws RangeError
When estimates holds fewer than two values — throws RangeError

Complexity: time O(n + m), space O(n + m).

Worked example#

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

Input#

input

{
  "sample": [2, 3, 4, 3, 4],
  "estimates": [3, 3.1, 3.2, 3.3, 3.4],
  "populationMean": 3.2,
  "alpha": 0.05,
  "mseBenchmark": 0.1,
  "nullMean": 3,
  "alternativeMean": 3.5,
  "practicalThreshold": 0.1,
  "comparisons": 5
}

Call#

centralLimitTheorem(input)

Returns#

object with 2 fields: standardizedMeans, center

{
  "standardizedMeans": [
    -1.2649110640673535,
    -0.6324555320336768,
    0,
    0.6324555320336739,
    1.2649110640673507
  ],
  "center": -1.1546319456101628e-15
}