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Independence and Dependence

Install and import#

bash
npm install fintech-algorithms
ts
import { independenceAndDependence } from "fintech-algorithms/foundations/probability-and-random-variables/independence-and-dependence";

Signature#

independenceAndDependence(input)

Compares the observed joint probability of two events against the product of their marginals, and reports both the verdict and the size of the gap.

Parameters#

NameTypeNotes
input{ pA: number; pB: number; pAB: number }pA and pB are the marginal probabilities and pAB the joint probability actually observed.
pA: 0 <= pA <= 1 · pB: 0 <= pB <= 1 · pAB: 0 <= pAB <= min(pA, pB)

Returns#

{ independent: boolean; dependenceGap: number }

independent is true when |pAB - pA * pB| is under 1e-12, and dependenceGap is the signed difference pAB - pA * pB, positive when the events co-occur more often than independence would imply.

Errors#

  • When input is null, an array, or not an object — throws TypeError
  • When pA, pB, or pAB falls outside [0, 1], or pAB exceeds min(pA, pB) — throws RangeError

Complexity: time O(1), space O(1).

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
{
  "pA": 0.6,
  "pB": 0.5,
  "pAB": 0.3,
  "outcomes": ["up", "flat", "down"],
  "event": ["up", "flat"],
  "prior": 0.01,
  "sensitivity": 0.9,
  "falsePositiveRate": 0.05,
  "randomValues": [0, 1, 2],
  "probabilities": [0.2, 0.5, 0.3],
  "randomVariableKind": "discrete",
  "joint": [
    {
      "x": 0,
      "y": 0,
      "p": 0.3
    },
    {
      "x": 0,
      "y": 1,
      "p": 0.2
    },
    {
      "x": 1,
      "y": 0,
      "p": 0.1
    }
  ],
  "conditionY": 1
}

Call#

independenceAndDependence(input)

Returns#

object with 2 fields: independent, dependenceGap

{
  "independent": true,
  "dependenceGap": 0
}

Diagrams#

Independence and Dependence — article hero
Independence and Dependence — calculation ledger
Independence and Dependence — concept anatomy
Independence and Dependence — failure boundary
Independence and Dependence — method map
Independence and Dependence — 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 Probability and Random Variables family#