Quantile — where it appears
Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.
The promise that does not survive the tree
A high-biased quantile summary at ε = 1% answers the 99th percentile of twenty thousand values to within two ranks. Merge thirty-two of them and the answer is seventeen ranks out — inside the merged bound, eight times outside the one anybody was quoted.
An error measured against the answer
A quantile summary asked for the 99.9th percentile answered 9,694 where the truth was 256, and violated nothing — its promise was a rank error under one per cent of the stream and it delivered a tenth of one per cent. One per cent of the stream is a thousand per cent of the tail, and no amount of extra state changes that.
The digest that promises nothing
The t-digest is the quantile structure most widely deployed and the only one with no proven bound on its rank error at any quantile. Measured, it beats the structure that does have one — and on two clusters with a gap between them it returns 431.5, where the data holds nothing at all between 40 and 800.
Named alongside it
The objects these essays reach for when they reach for this one.
GuaranteeRank errorTailGreenwald–KhannaHeavy tailMeasurementState bitsSummaryCounterexampleEpsilonEstimatorFalsification