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Bernoulli and Binomial Distributions

Install and import#

bash
npm install fintech-algorithms
ts
import { bernoulliAndBinomialDistributions } from "fintech-algorithms/foundations/probability-distributions-and-simulation-basics/bernoulli-and-binomial-distributions";

Signature#

bernoulliAndBinomialDistributions(input)

Computes the Bernoulli mean and the binomial probability mass and cumulative probability for k successes in n independent trials with success probability p.

Parameters#

NameTypeNotes
inputD00InputOne record carrying p (success probability of a single trial), n (number of trials) and k (number of successes to evaluate).
p: between 0 and 1 inclusive · n: integer, zero or greater · k: integer, between 0 and n inclusive

Returns#

D00Output

An object with bernoulliMean (equal to p), binomialPmf (the mass at exactly k) and binomialCdf (the mass summed from zero through k).

Errors#

  • When p is missing or outside 0 to 1 — this check runs for every topic in the family — throws RangeError
  • When n or k is not an integer, n is negative, k is negative, or k exceeds n — throws RangeError

Complexity: time O(n*k), space O(k).

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": [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#

bernoulliAndBinomialDistributions(input)

Returns#

object with 2 fields: bernoulliMean, binomialPmf

{
  "bernoulliMean": 0.3,
  "binomialPmf": 0.3086999999999999
}

Diagrams#

Bernoulli and Binomial Distributions — article hero
Bernoulli and Binomial Distributions — calculation ledger
Bernoulli and Binomial Distributions — concept anatomy
Bernoulli and Binomial Distributions — failure boundary
Bernoulli and Binomial Distributions — method map
Bernoulli and Binomial Distributions — 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 Distributions and Simulation Basics family#