tdigest
Javascript implementation of Dunning's TDigest for streaming quantile approximation
The TDigest is a data structure and algorithm for constructing an approximate distribution for a collection of real numbers presented as a stream. The algorithm makes no guarantees, but behaves well enough in practice that implementations have been included in Apache Mahout and ElasticSearch for computing summaries and approximate order statistics over a stream.
For an overview of TDigest's behavior, see DavidsonPilon's blog post regarding a python implementation. For more details, there are the tdigest paper and reference implementation (Java). This javascript implementation is based on a reading of the paper, with some boundary and performance tweaks.
changes in 0.1.2:
Updated the bintree dependency to 1.0.2 to pick up its licencing declaration
changes in 0.1.1:

percentile on an empty digest returns undefined or array of undefined instead of NaN

upgraded bintrees to get bugfix.

bugfix for discrete percentile and p_rank, make boundary conditions conform to standard definition.
changes in 0.1.0:
Discrete mode: when a TDigest is created with delta=false, the sample distribution is treated as discrete. TDigest behavior is disabled, differing samples are never merged (they needn't even be numeric), and percentiles are reported as nearest exact data values rather than interpolated.
Digest: distribution digest structure. Starts in exact histogram (discrete) mode, remains in exact mode for reasonable numbers of distinct values as sample size inreases, and automatically switches to TDigest mode for large samples that appear to be from a continuous distribution.
Renamed quantile() > p_rank(), Percentile Rank.
percentile() and p_rank() now accept arrays or singleton arguments.
changes in 0.0.7:
A grunt dist
task has been added to create a UMDwrapped version of tdigest
and dependencies for importing as a standalone module in clientside javascript.
bugfixes and speed improvements.
changes in 0.0.5:
API Overhaul:
 asArray() > toArray()
 redigest() > compress()
 digest() > push()
 pushing an array no longer triggers compression
bugfixes and speed improvements.
quickstart
node.js:
npm install tdigest
var TDigest = require('tdigest').TDigest;
var x=[], N = 100000;
for (var i = 0 ; i < N ; i += 1) {
x.push(Math.random() * 10  5);
};
td = new TDigest();
td.push(x);
td.compress();
console.log(td.summary());
console.log("median ~ "+td.percentile(0.5));
See also example.js in this package.
In the browser:
The grunt dist
task has been configured to generate
a selfcontained UMDwrapped version of tdigest in dist/tdigest.js.
Embed it in HTML like this:
<script src="dist/tdigest.js"></script>
<script>
var td = new this.tdigest.TDigest();
for (var i=0; i < 1000000; i++) {
td.push(Math.random());
}
td.compress();
document.write(td.summary())
</script>
See also example.html in this package.
dependencies
bintrees
: https://www.npmjs.com/package/bintrees