# Quantile Estimation (DDSketch) > Depth-first rabbithole dossier for Quantile Estimation (DDSketch); source-anchored research pack. Parent: [Client Side Operations Timeout (CSOT)](https://llms-explorer.com/tree/client-side-operations-timeout-csot/) · 4 facets · 7 facts · page: https://llms-explorer.com/tree/quantile-estimation-ddsketch/ ## Definitions - [low] The bucket index for DDSketch is calculated as ceil(ln(value) / ln(gamma)), where gamma is defined as (1 + alpha) / (1 - alpha) and alpha represents the desired relative accuracy. Sources: https://infoq.com/articles/adaptive-hedged-requests-p99-latency — source: `~/.global-ai-hub/research/.pipeline/mongodb-2026-10-14/frb/quantile-estimation-ddsketch-3c9ec6b95e/rabbithole-synthesis.md#methodology` ## How it works - [low] DDSketch is capable of handling endpoints that process over 10M points per second, providing accurate latency quantiles for these high-throughput scenarios. Sources: https://ar5iv.labs.arxiv.org/html/1908.10693 — source: `~/.global-ai-hub/research/.pipeline/mongodb-2026-10-14/frb/quantile-estimation-ddsketch-3c9ec6b95e/rabbithole-synthesis.md#core` - [low] The MongoDB $percentile accumulator requires quantile elements in p to be numeric values in the range 0.0 to 1.0 inclusive, and because its t-digest approximation uses pseudorandomness, computed percentile values on the same dataset might differ on each run. Sources: https://www.mongodb.com/docs/manual/reference/operator/aggregation/percentile.md — source: `~/.global-ai-hub/research/.pipeline/mongodb-2026-10-14/frb/quantile-estimation-ddsketch-3c9ec6b95e/rabbithole-synthesis.md#core` ## Problems, failure modes and limitations - [high] DDSketch is the first fully-mergeable, relative-error quantile sketching algorithm with formal guarantees, providing O(1) constant-memory quantile estimation with relative-error guarantees of plus or minus one percent. Sources: https://ar5iv.labs.arxiv.org/html/1908.10693, https://infoq.com/articles/adaptive-hedged-requests-p99-latency — source: `~/.global-ai-hub/research/.pipeline/mongodb-2026-10-14/frb/quantile-estimation-ddsketch-3c9ec6b95e/rabbithole-synthesis.md#core` ## Facts and statements - [high] DDSketch has a critical-path overhead of approximately thirty-five nanoseconds per request, making it suitable for real-time per-host latency tracking, and can accurately maintain upper half order statistics of over a million samples with a sketch size of 273 with probability greater than 0.99991. Sources: https://ar5iv.labs.arxiv.org/html/1908.10693, https://infoq.com/articles/adaptive-hedged-requests-p99-latency — source: `~/.global-ai-hub/research/.pipeline/mongodb-2026-10-14/frb/quantile-estimation-ddsketch-3c9ec6b95e/rabbithole-synthesis.md#core` - [low] Adding a hundred million values to an empty DDSketch takes less than 5 seconds on a 3.1GHz MacBook Pro, while merging two DDSketches containing up to fifty million values each takes around 10 microseconds or less. Sources: https://ar5iv.labs.arxiv.org/html/1908.10693 — source: `~/.global-ai-hub/research/.pipeline/mongodb-2026-10-14/frb/quantile-estimation-ddsketch-3c9ec6b95e/rabbithole-synthesis.md#methodology` - [low] A tumbling window fix uses two DDSketches rotating at a fixed interval, such as thirty seconds, to manage data aging. Sources: https://infoq.com/articles/adaptive-hedged-requests-p99-latency — source: `~/.global-ai-hub/research/.pipeline/mongodb-2026-10-14/frb/quantile-estimation-ddsketch-3c9ec6b95e/rabbithole-synthesis.md#methodology` ## Related concepts - DDSketch — is a part of Quantile Estimation (DDSketch) - Quantile — is a part of Quantile Estimation (DDSketch) - Estimation — is a part of Quantile Estimation (DDSketch)