Exponential distribution prob API

Evaluates the exponential distribution: CDF/survival/PDF at x or an interval probability, plus mean, median and variance. Answers 'What is the probability of waiting less than t with this rate?', 'What is the survival probability of an exponential lifetime?'.

Price$0.04per request

MethodPOST

Route/v1/stats/exponential-probability

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

statisticsexponentialdistributionprobabilitycdfsurvivalreliabilitywaiting-time

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

Integration docs

Example request

{
  "rate": 0.5,
  "x": 2
}

Example response

{
  "rate": 0.5,
  "x": 2,
  "cdf": 0.63212056,
  "survival": 0.36787944,
  "pdf": 0.18393972,
  "mean": 2,
  "median": 1.386294,
  "variance": 4,
  "rating": "past median",
  "interpretation": "P(X ≤ 2) = 0.63212, survival = 0.36788 for Exponential(λ=0.5)."
}

Input schema

{
  "type": "object",
  "required": [
    "rate"
  ],
  "properties": {
    "rate": {
      "type": "number",
      "examples": [
        0.5
      ]
    },
    "x": {
      "type": "number",
      "examples": [
        2
      ]
    },
    "lower": {
      "type": "number"
    },
    "upper": {
      "type": "number"
    }
  }
}

Output schema

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