npm package: @stdlib/stats-incr-mmeanvar
Description: Compute a moving arithmetic mean and unbiased sample variance incrementally.
Author: The Stdlib Authors
Latest version: 0.2.3

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  <summary>
    About stdlib...
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# incrmmeanvar

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute a moving [arithmetic mean][arithmetic-mean] and [unbiased sample variance][sample-variance] incrementally.

<section class="intro">

For a window of size `W`, the [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" data-equation="eq:arithmetic_mean">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@c8c3c87eeab590bfdff924ec0fb269fb33a7de2b/lib/node_modules/@stdlib/stats/incr/mmeanvar/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
    <br>
</div> -->

<!-- </equation> -->

and the [unbiased sample variance][sample-variance] is defined as

<!-- <equation class="equation" label="eq:unbiased_sample_variance" align="center" raw="s^2 = \frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2" alt="Equation for the unbiased sample variance."> -->

<!-- <div class="equation" align="center" data-raw-text="s^2 = \frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2" data-equation="eq:unbiased_sample_variance">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@563a8587d936008c82db675be84f8ce1474fee27/lib/node_modules/@stdlib/stats/incr/mmeanvar/docs/img/equation_unbiased_sample_variance.svg" alt="Equation for the unbiased sample variance.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-incr-mmeanvar
```

</section>

<section class="usage">

## Usage

```javascript
var incrmmeanvar = require( '@stdlib/stats-incr-mmeanvar' );
```

#### incrmmeanvar( \[out,] window )

Returns an accumulator `function` which incrementally computes a moving [arithmetic mean][arithmetic-mean] and [unbiased sample variance][sample-variance]. The `window` parameter defines the number of values over which to compute the moving [arithmetic mean][arithmetic-mean] and [unbiased sample variance][sample-variance].

```javascript
var accumulator = incrmmeanvar( 3 );
```

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.

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

var accumulator = incrmmeanvar( new Float64Array( 2 ), 3 );
```

#### 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.

```javascript
var accumulator = incrmmeanvar( 3 );

var out = accumulator();
// returns null

// Fill the window...
out = accumulator( 2.0 ); // [2.0]
// returns [ 2.0, 0.0 ]

out = accumulator( 1.0 ); // [2.0, 1.0]
// returns [ 1.5, 0.5 ]

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

// Window begins sliding...
out = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
// returns [ -1.0, 28.0 ]

out = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
// returns [ -3.0, 28.0 ]

out = accumulator();
// returns [ -3.0, 28.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Input values are **not** type checked. If provided `NaN`, the accumulated values are `NaN` for **at least** `W-1` 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.
-   As `W` values are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random-base-randu' );
var Float64Array = require( '@stdlib/array-float64' );
var ArrayBuffer = require( '@stdlib/array-buffer' );
var incrmmeanvar = require( '@stdlib/stats-incr-mmeanvar' );

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( incrmmeanvar( out, 5 ) );
}

// Simulate data and update the moving 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 ) );
}
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/stats-incr/meanvar`][@stdlib/stats/incr/meanvar]</span><span class="delimiter">: </span><span class="description">compute an arithmetic mean and unbiased sample variance incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/mmean`][@stdlib/stats/incr/mmean]</span><span class="delimiter">: </span><span class="description">compute a moving arithmetic mean incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/mmeanstdev`][@stdlib/stats/incr/mmeanstdev]</span><span class="delimiter">: </span><span class="description">compute a moving arithmetic mean and corrected sample standard deviation incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/mvariance`][@stdlib/stats/incr/mvariance]</span><span class="delimiter">: </span><span class="description">compute a moving unbiased sample variance incrementally.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].

#### Community

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-mmeanvar/main/LICENSE

[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean

[sample-variance]: https://en.wikipedia.org/wiki/Variance

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[@stdlib/stats/incr/mmean]: https://www.npmjs.com/package/@stdlib/stats-incr-mmean

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