Poisson probability API

Compute Poisson probabilities P(X=k)=λ^k e^(−λ)/k! for rate λ, including exact, at-most (CDF) and at-least, with mean and variance both equal to λ. Auditable: returns all three modes. Answers 'probability of exactly 2 events when rate is 3','at most 1 arrival','Poisson CDF'.

Price$0.01per request

MethodPOST

Route/v1/calc/stat-poisson-probability

StatusLive

MIME typeapplication/json

Rate limit120/minute

CacheNo cache

calcstatisticspoissonprobabilitypmfcdfratedistribution

API URLhttps://x402.hexl.dev/v1/calc/stat-poisson-probability

Integration docs

Example request

{
  "lambda": 3,
  "k": 2
}

Example response

{
  "lambda": 3,
  "k": 2,
  "mode": "exact",
  "probability": 0.22404181,
  "exact": 0.22404181,
  "atMost": 0.42319008,
  "atLeast": 0.80085173,
  "mean": 3,
  "variance": 3,
  "rating": "plausible",
  "interpretation": "P(X = 2) = 0.224042 for Poisson(λ=3)."
}

Input schema

{
  "type": "object",
  "required": [
    "lambda",
    "k"
  ],
  "properties": {
    "lambda": {
      "type": "number",
      "description": "mean rate λ (>=0)",
      "examples": [
        3
      ]
    },
    "k": {
      "type": "number",
      "description": "event count (>=0 integer)",
      "examples": [
        2
      ]
    },
    "cumulative": {
      "type": "string",
      "enum": [
        "exact",
        "atMost",
        "atLeast"
      ],
      "default": "exact"
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}