fintech-algorithms
/
Using a coding agent? Give it the skill: npx skills add IslamBaraka90/Fintech-Algorithms-Library What it does →

Skewness and Tail Asymmetry

Install and import#

bash
npm install fintech-algorithms
ts
import { skewnessAndTailAsymmetry } from "fintech-algorithms/foundations/dispersion-shape-and-robust-statistics/skewness-and-tail-asymmetry";

Signature#

skewnessAndTailAsymmetry(input)

Divides the third central moment by the second raised to the power 1.5, giving the moment coefficient of skewness, and labels which tail is the longer one.

Parameters#

NameTypeNotes
input{ values: number[] }The observations whose asymmetry is being measured, under the key values. Both moments are population moments, dividing by n rather than applying a small-sample correction.
values: at least two observations, and not all identical

Returns#

{ momentSkewness: number; direction: 'right' | 'left' | 'symmetric' }

momentSkewness is m3 / m2 ** 1.5, and direction is right when it is positive, left when negative, and symmetric at exactly zero.

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 values holds fewer than two observations, so the sample divisor n - 1 would be zero — throws RangeError
  • When the second central moment is zero because every observation is identical — throws RangeError

Complexity: time O(n log n), space O(n).

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
{
  "values": [1, 2, 2, 4, 9]
}

Call#

skewnessAndTailAsymmetry(input)

Returns#

object with 2 fields: momentSkewness, direction

{
  "momentSkewness": 1.1140963830468877,
  "direction": "right"
}

Diagrams#

Skewness and Tail Asymmetry — article hero
Skewness and Tail Asymmetry — calculation ledger
Skewness and Tail Asymmetry — concept anatomy
Skewness and Tail Asymmetry — failure boundary
Skewness and Tail Asymmetry — method map
Skewness and Tail Asymmetry — scenario contrast

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

The rest of the Dispersion, Shape, and Robust Statistics family#