stats-logscale

A memory-efficient approximate statistical analysis tool using logarithmic binning.

Example: repeated setTimeout(0) execution times

Description

data is split into bins (aka buckets), linear close to zero and logarithmic for large numbers (hence the name), thus maintaining desired absolute and relative precision;
can calculate mean, variance, median, moments, percentiles, cumulative distribution function (i.e. probability that a value is less than x), and expected values of arbitrary functions over the sample;
can generate histograms for plotting the data;
all calculated values are cached. Cache is reset upon adding new data;
(almost) every function has a "neat" counterpart which rounds the result to the shortest possible number within the precision bounds. E.g. foo.mean() // 1.0100047, but foo.neat.mean() // 1.01;
is (de)serializable;
can split out partial data or combine multiple samples into one.

Usage

Creating the sample container:

const { Univariate } = require( 'stats-logscale' );
const stat = new Univariate();

Specifying absolute and relative precision. The defaults are 10^-9 and 1.001, respectivele. Less precision = less memory usage and faster data querying (but not insertion).

const stat = new Univariate({base: 1.01, precision: 0.001});

Use flat switch to avoid using logarithmic binning at all:

// this assumes the data is just integer numbers
const stat = new Univariate({precision: 1, flat: true});

Adding data points, wither one by one, or as (value, frequency) pairs. Strings are OK (e.g. after parsing user input) but non-numeric values will cause an exception:

stat.add (3.14);
stat.add ("Foo"); // Nope!
stat.add ("3.14 3.15 3.16".split(" "));
stat.addWeighted([[0.5, 1], [1.5, 3], [2.5, 5]]);

Querying data:

stat.count();           // number of data points
stat.mean();            // average
stat.stdev();           // standard deviation
stat.median();          // half of data is lower than this value
stat.percentile(90);    // 90% of data below this point
stat.quantile(0.9);     // ditto
stat.cdf(0.5);          // Cumulative distribution function, which means
                        // the probability that a data point is less than 0.5
stat.moment(power);     // central moment of an integer power
stat.momentAbs(power);  // < |x-<x>| ** power >, power may be fractional
stat.E( x => x\*x );    // expected value of an arbitrary function

Each querying primitive has a "neat" counterpart that rounds its output to the shortest possible decimal number in the respective bin:

stat.neat.mean();
stat.neat.stdev();
stat.neat.median();

Extract partial samples:

stat.clone( { min: 0.5, max: 0.7 } );
stat.clone( { ltrim: 1, rtrim: 1 });
    // cut off outer 1% of data
stat.clone( { ltrim: 1, rtrim: 1, winsorize: true }});
    // ditto but truncate outliers instead of discarding

Serialize, deserialize, and combine data from multiple sources

const str = JSON.stringify(stat);
// send over the network here
const copy = new Univariate (JSON.parse(str));

main.addWeighted( partialStat.getBins() );
main.addWeighted( JSON.parse(str).bins ); // ditto

Create histograms and plot data:

stat.histogram({scale: 768, count:1024});
    // this produces 1024 bars of the form
    // [ bar_height, lower_boundary, upper_boundary ]
    // The intervals are consecutive.
    // The bar heights are limited to 768.

stat.histogram({scale: 70, count:20})
    .map( x => stat.shorten(x[1], x[2]) + '\t' + '+'.repeat(x[0]) )
    .join('\n')
    // "Draw" a vertical histogram for text console
    // You'll use PNG in production instead, right? Right?

See the playground.

Performance

Data inserts are optimized for speed, and querying is cached where possible. The script example/speed.js can be used to benchmark the module on your system.

Memory usage for a dense sample spanning 6 orders of magnitude was around 1.6MB in Chromium, ~230KB for the data itself + ~1.2MB for the cache.

Bugs

Please report bugs and request features via the github bugtracker.

Copyright and license