package tdigest

Tdigest

OCaml implementation of the T-Digest algorithm.

let td =
  Tdigest.create ()
  |> Tdigest.add_list [ 10.0; 11.0; 12.0; 13.0 ]
in

Tdigest.percentiles td [ 0.; 0.25; 0.5; 0.75; 1. ]
(* [ Some 10; Some 10.5; Some 11.5; Some 12.5; Some 13 ] *)

Tdigest.p_ranks td [ 9.; 10.; 11.; 12.; 13.; 14. ]
(* [ Some 0; Some 0.125; Some 0.375; Some 0.625; Some 0.875; Some 1 ] *)

The T-Digest is a data structure and algorithm for constructing an approximate distribution for a collection of real numbers presented as a stream.

The median of a list of medians is not necessarily equal to the median of the whole dataset. The median (p50), p95, and p99 are critical measures that are expensive to compute due to their requirement of having the entire sorted dataset present in one place.

The T-Digest can estimate percentiles or quantiles extremely accurately even at the tails, while using a fraction of the space.

Additionally, the T-Digest is concatenable, making it a good fit for distributed systems. The internal state of a T-Digest can be exported as a binary string, and the concatenation of any number of those strings can then be imported to form a new T-Digest.

let combined = Tdigest.merge [ td1; td2; td3 ] in

A T-Digest's state can be stored in a database VARCHAR/TEXT column and multiple such states can be merged by concatenating strings:

SELECT
  STRING_AGG(M.tdigest_state) AS concat_state
FROM my_table AS M

let combined = Tdigest.of_string concat_state in

Links:

• A simple overview of the T-Digest

• A walkthrough of the algorithm by its creator

• The white paper

This library started off as a port of Will Welch's JavaScript implementation, down to the unit tests. However some modifications have been made to adapt it to OCaml, the most important one being immutability. As such, almost every function in the Tdigest module return a new Tdigest.t, including "reading" ones since they may trigger intermediate computations worth caching.

Usage

The API is well documented here.

opam install tdigest

Performance

On a 2018 MacBook Pro, it can incorporate 1,000,000 random floating points in just 770ms.

Exporting and importing state (to_string/of_string) is essentially free.