{
  "slug": "quantile",
  "term": "Quantile",
  "aliases": [
    "percentile"
  ],
  "definition": "A quantile is a distribution threshold associated with a specified cumulative probability, whose estimate from a finite sample depends on the chosen convention.",
  "note": "For a distribution function F, the generalized inverse defines q_p as the smallest x for which F(x) is at least p. The inverse empirical CDF (type 1) selects a ranked observation; interpolated estimators can instead return a value between observations. Record the estimator, sample count and timing population when reporting storage p99. [r-quantile]\n\nProbability position and value precision are different. Under a fixed-size IID continuous-population model, the maximum of n samples covers the population q_p with probability 1-p^n. This does not bound a percentile estimator's error in milliseconds; correlated latency bursts violate the independence assumption. [hesela-sampling]",
  "related": [
    "tail-latency",
    "latency-storage",
    "confidence-interval"
  ],
  "citations": [
    {
      "id": "r-quantile",
      "title": "R stats documentation: Sample Quantiles, type 1 inverse empirical CDF and floating-point rounding safeguards.",
      "url": "https://stat.ethz.ch/R-manual/R-devel/library/stats/html/quantile.html",
      "accessed": "2026-10-17"
    },
    {
      "id": "hesela-sampling",
      "title": "Hesela: tail sampling probabilities, explicit IID assumptions and reproducible analytic results",
      "url": "https://hesela.com/analyses/storage-latency-coordinated-omission/#tail-sampling",
      "accessed": "2026-10-17"
    }
  ],
  "status": "research",
  "advantages": [],
  "limitations": [],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "updated": "2026-10-17"
}