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2019

Computing Extremely Accurate Quantiles Using t-Digests

Dunning, Ted, Ertl, Otmar

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We present on-line algorithms for computing approximations of rank-based statistics that give high accuracy, particularly near the tails of a distribution, with very small sketches.

Notably, the method allows a quantile $q$ to be computed with an accuracy relative to $\max(q, 1-q)$ rather than absolute accuracy as with most other methods.
This new algorithm is robust with respect to skewed distributions or ordered datasets and allows separately computed summaries to be combined with no loss in accuracy.
An open-source Java implementation of this algorithm is available from the author.

Computing Extremely Accurate Quantiles Using t-Digests · Around

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Selection and sorting with limited storage
Munro, J.I., & Paterson, M.S. 1980 · 1980
Earlier work this paper cites.
Incremental Quantile Estimation for Massive Tracking
Chen, Fei, Lambert, Diane, & Pinheiro, José C. 2000 · 2000
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Space-efficient Online Computation of Quantile Summaries
Greenwald, Michael, & Khanna, Sanjeev. 2001 · 2001
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