Hypergeometric distribution API

Computes hypergeometric probabilities for k successes in n draws without replacement from a population of N with K successes (exact/at-most/at-least), plus mean and variance. Answers 'What is the probability of drawing k specific items without replacement?', 'What is the hypergeometric PMF?'.

Price$0.06per request

MethodPOST

Route/v1/stats/hypergeometric-probability

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

statisticshypergeometricdistributionprobabilitywithout-replacementsamplingpmfdiscrete

API URLhttps://x402.hexl.dev/v1/stats/hypergeometric-probability

Integration docs

Example request

{
  "N": 50,
  "K": 5,
  "n": 10,
  "k": 1
}

Example response

{
  "N": 50,
  "K": 5,
  "n": 10,
  "k": 1,
  "mode": "exact",
  "probability": 0.4313372,
  "exact": 0.4313372,
  "atMost": 0.74189998,
  "atLeast": 0.68943722,
  "mean": 1,
  "variance": 0.734694,
  "rating": "plausible",
  "interpretation": "Hypergeometric(N=50,K=5,n=10): P(X = 1) = 0.431337."
}

Input schema

{
  "type": "object",
  "required": [
    "N",
    "K",
    "n",
    "k"
  ],
  "properties": {
    "N": {
      "type": "integer",
      "examples": [
        50
      ]
    },
    "K": {
      "type": "integer",
      "examples": [
        5
      ]
    },
    "n": {
      "type": "integer",
      "examples": [
        10
      ]
    },
    "k": {
      "type": "integer",
      "examples": [
        1
      ]
    },
    "cumulative": {
      "type": "string",
      "enum": [
        "exact",
        "atMost",
        "atLeast"
      ]
    }
  }
}

Output schema

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