npm package: @stdlib/stats-incr-ewvariance
Description: Compute an exponentially weighted variance incrementally.
Author: The Stdlib Authors
Latest version: 0.2.3

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</details>

# increwvariance

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

> Compute an [exponentially weighted variance][moving-average] incrementally.

<section class="intro">

An [exponentially weighted variance][moving-average] can be defined recursively as

<!-- <equation class="equation" label="eq:exponentially_weighted_variance" align="center" raw="S_n = \begin{cases} 0 & \textrm{if}\ n = 0 \\ (1 - \alpha) (S_{n-1} + \alpha(x_n - \mu_{n-1})^2) & \textrm{if}\ n > 0 \end{cases}" alt="Recursive definition for computing an exponentially weighted variance."> -->

<div class="equation" align="center" data-raw-text="S_n = \begin{cases} 0 &amp; \textrm{if}\ n = 0 \\ (1 - \alpha) (S_{n-1} + \alpha(x_n - \mu_{n-1})^2) &amp; \textrm{if}\ n &gt; 0 \end{cases}" data-equation="eq:exponentially_weighted_variance">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@12be48682a7c25918504f886cbb80051c6ec8240/lib/node_modules/@stdlib/stats/incr/ewvariance/docs/img/equation_exponentially_weighted_variance.svg" alt="Recursive definition for computing an exponentially weighted variance.">
    <br>
</div>

<!-- </equation> -->

where `μ` is the [exponentially weighted mean][@stdlib/stats/incr/ewmean].

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

```javascript
var increwvariance = require( '@stdlib/stats-incr-ewvariance' );
```

#### increwvariance( alpha )

Returns an accumulator `function` which incrementally computes an [exponentially weighted variance][moving-average], where `alpha` is a smoothing factor between `0` and `1`.

```javascript
var accumulator = increwvariance( 0.5 );
```

#### accumulator( \[x] )

If provided an input value `x`, the accumulator function returns an updated variance. If not provided an input value `x`, the accumulator function returns the current variance.

```javascript
var accumulator = increwvariance( 0.5 );

var v = accumulator();
// returns null

v = accumulator( 2.0 );
// returns 0.0

v = accumulator( 1.0 );
// returns 0.25

v = accumulator( 3.0 );
// returns 0.6875

v = accumulator();
// returns 0.6875
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random-base-randu' );
var increwvariance = require( '@stdlib/stats-incr-ewvariance' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = increwvariance( 0.5 );

// For each simulated datum, update the exponentially weighted variance...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
}
console.log( accumulator() );
```

</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/ewmean`][@stdlib/stats/incr/ewmean]</span><span class="delimiter">: </span><span class="description">compute an exponentially weighted mean incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/ewstdev`][@stdlib/stats/incr/ewstdev]</span><span class="delimiter">: </span><span class="description">compute an exponentially weighted standard deviation incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/variance`][@stdlib/stats/incr/variance]</span><span class="delimiter">: </span><span class="description">compute an unbiased sample variance 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 -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->


<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

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

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[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/stats-incr-ewvariance/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-incr-ewvariance/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-incr-ewvariance/tree/umd
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-ewvariance/main/LICENSE

[moving-average]: https://en.wikipedia.org/wiki/Moving_average

<!-- <related-links> -->

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

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

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

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

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</section>

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