quantile · research · also percentile

Quantile

A quantile is a distribution threshold associated with a specified cumulative probability, whose estimate from a finite sample depends on the chosen convention.

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. [1]

Probability 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. [2]

Relations

related

tail-latency, latency-storage, confidence-interval

Citations

1. R stats documentation: Sample Quantiles, type 1 inverse empirical CDF and floating-point rounding safeguards. (accessed 2026-10-17)
2. Hesela: tail sampling probabilities, explicit IID assumptions and reproducible analytic results (accessed 2026-10-17)

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