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Poisson Distribution and Event Counts

Install and import#

bash
npm install fintech-algorithms
ts
import { poissonDistributionAndEventCounts } from "fintech-algorithms/foundations/probability-distributions-and-simulation-basics/poisson-distribution-and-event-counts";

Signature#

poissonDistributionAndEventCounts(input)

Evaluates the Poisson probability of exactly k events, the cumulative probability of at most k, and the distribution's mean and variance, for a rate of lambda events per interval.

Parameters#

NameTypeNotes
inputD00InputOne record carrying lambda (the expected event count per interval), k (the event count to evaluate) and p, which the family entry point validates before dispatching.
lambda: zero or greater · k: integer, zero or greater · p: between 0 and 1 inclusive

Returns#

D00Output

An object with pmf (probability of exactly k events), cdf (probability of at most k), and mean and variance, both equal to lambda.

Errors#

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

Complexity: time O(k^2), 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#

poissonDistributionAndEventCounts(input)

Returns#

object with 2 fields: pmf, cdf

{
  "pmf": 0.2706705664732254,
  "cdf": 0.6766764161830635
}

Diagrams#

Poisson Distribution and Event Counts — article hero
Poisson Distribution and Event Counts — calculation ledger
Poisson Distribution and Event Counts — concept anatomy
Poisson Distribution and Event Counts — failure boundary
Poisson Distribution and Event Counts — method map
Poisson Distribution and Event Counts — 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#