README.md

About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

incrmeanvar

Compute an arithmetic mean and an unbiased sample variance incrementally.

The arithmetic mean is defined as

$$\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i$$

and the unbiased sample variance is defined as

$$s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2$$

Installation

npm install @stdlib/stats-incr-meanvar

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var incrmeanvar = require( '@stdlib/stats-incr-meanvar' );

incrmeanvar( [out] )

Returns an accumulator function which incrementally computes an arithmetic mean and unbiased sample variance.

var accumulator = incrmeanvar();

By default, the returned accumulator function returns the accumulated values as a two-element array. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.

var Float64Array = require( '@stdlib/array-float64' );

var accumulator = incrmeanvar( new Float64Array( 2 ) );

accumulator( [x] )

If provided an input value x, the accumulator function returns updated accumulated values. If not provided an input value x, the accumulator function returns the current accumulated values.

var accumulator = incrmeanvar();

var mv = accumulator();
// returns null

mv = accumulator( 2.0 );
// returns [ 2.0, 0.0 ]

mv = accumulator( 1.0 );
// returns [ 1.5, 0.5 ]

mv = accumulator( 3.0 );
// returns [ 2.0, 1.0 ]

mv = accumulator( -7.0 );
// returns [ -0.25, ~20.92 ]

mv = accumulator( -5.0 );
// returns [ -1.2, 20.2 ]

mv = accumulator();
// returns [ -1.2, 20.2 ]

Notes

• Input values are not type checked. If provided NaN, the accumulated values are equal to NaN for all future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.

Examples

var randu = require( '@stdlib/random-base-randu' );
var Float64Array = require( '@stdlib/array-float64' );
var ArrayBuffer = require( '@stdlib/array-buffer' );
var incrmeanvar = require( '@stdlib/stats-incr-meanvar' );

var offset;
var acc;
var buf;
var out;
var mv;
var N;
var v;
var i;
var j;

// Define the number of accumulators:
N = 5;

// Create an array buffer for storing accumulator output:
buf = new ArrayBuffer( N*2*8 ); // 8 bytes per element

// Initialize accumulators:
acc = [];
for ( i = 0; i < N; i++ ) {
    // Compute the byte offset:
    offset = i * 2 * 8; // stride=2, bytes_per_element=8

    // Create a new view for storing accumulated values:
    out = new Float64Array( buf, offset, 2 );

    // Initialize an accumulator which will write results to the view:
    acc.push( incrmeanvar( out ) );
}

// Simulate data and update the sample means and variances...
for ( i = 0; i < 100; i++ ) {
    for ( j = 0; j < N; j++ ) {
        v = randu() * 100.0 * (j+1);
        acc[ j ]( v );
    }
}

// Print the final results:
console.log( 'Mean\tVariance' );
for ( i = 0; i < N; i++ ) {
    mv = acc[ i ]();
    console.log( '%d\t%d', mv[ 0 ].toFixed( 3 ), mv[ 1 ].toFixed( 3 ) );
}

---

See Also

• @stdlib/stats-incr/mean: compute an arithmetic mean incrementally.
• @stdlib/stats-incr/meanstdev: compute an arithmetic mean and corrected sample standard deviation incrementally.
• @stdlib/stats-incr/mmeanvar: compute a moving arithmetic mean and unbiased sample variance incrementally.
• @stdlib/stats-incr/variance: compute an unbiased sample variance incrementally.

---

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

---

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.