Prediction & tolerance interval API

Computes a t-based prediction interval for the next single observation, or a normal two-sided tolerance interval (Howe k-factor) that covers a target fraction of the population with stated confidence — distinct from a confidence interval for the mean. Answers 'What range will the next observation fall in?', 'What interval covers 95% of the population with 95% confidence?'.

Price$0.06per request

MethodPOST

Route/v1/stats/prediction-interval

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

statisticsprediction-intervaltolerance-intervalforecastcoverageinferencefuture-observationk-factor

API URLhttps://x402.hexl.dev/v1/stats/prediction-interval

Integration docs

Example request

{
  "mean": 100,
  "sd": 15,
  "n": 25
}

Example response

{
  "kind": "prediction",
  "confidence": 0.95,
  "mean": 100,
  "sd": 15,
  "n": 25,
  "df": 24,
  "tCritical": 2.0639,
  "standardError": 15.297059,
  "lower": 68.428423,
  "upper": 131.571577,
  "interpretation": "95% prediction interval for the next observation: [68.4284, 131.5716]."
}

Input schema

{
  "type": "object",
  "required": [],
  "properties": {
    "data": {
      "type": "array",
      "items": {
        "type": "number"
      }
    },
    "mean": {
      "type": "number",
      "examples": [
        100
      ]
    },
    "sd": {
      "type": "number",
      "examples": [
        15
      ]
    },
    "n": {
      "type": "integer",
      "examples": [
        25
      ]
    },
    "confidence": {
      "type": "number",
      "examples": [
        0.95
      ]
    },
    "kind": {
      "type": "string",
      "enum": [
        "prediction",
        "tolerance"
      ]
    },
    "coverage": {
      "type": "number",
      "examples": [
        0.95
      ]
    }
  }
}

Output schema

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