The problems of having high relative errors on the larger quantiles has been addressed by a line of work that still uses rank error, but promises lower rank error on the quantiles further away from the median by biasing the data it keeps towards the higher (and lower) quantiles [7], [8], [17]. The latter, dubbed t-digest, is notable as it is one of the quantile sketch implementations used by Elasticsearch [18]. These sketches have much better accuracy (in rank)
than uniform-rank-error sketches on percentiles like the p99.9, but they still have high relative error on heavy-tailed data sets. Like GK they are only one-way mergeable.
The problems of having high relative errors on the larger quantiles has been addressed by a line of work that still uses rank error, but promises lower rank error on the quantiles further away from the median by biasing the data it keeps towards the higher (and lower) quantiles [7], [8], [17]. The latter, dubbed t-digest, is notable as it is one of the quantile sketch implementations used by Elasticsearch [18]. These sketches have much better accuracy (in rank) than uniform-rank-error sketches on percentiles like the p99.9, but they still have high relative error on heavy-tailed data sets. Like GK they are only one-way mergeable.