npm package: @stdlib/stats-incr-mstdev
Description: Compute a moving corrected sample standard deviation incrementally.
Author: The Stdlib Authors
Latest version: 0.2.3

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  <p>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.</p>
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</details>

# incrmstdev

[![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 [corrected sample standard deviation][standard-deviation] incrementally.

<section class="intro">

For a window of size `W`, the [corrected sample standard deviation][standard-deviation] is defined as

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

<div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2}" data-equation="eq:corrected_sample_standard_deviation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/mstdev/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for the corrected sample standard deviation.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

```javascript
var incrmstdev = require( '@stdlib/stats-incr-mstdev' );
```

#### incrmstdev( window\[, mean] )

Returns an accumulator `function` which incrementally computes a moving [corrected sample standard deviation][standard-deviation]. The `window` parameter defines the number of values over which to compute the moving [corrected sample standard deviation][standard-deviation].

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

If the mean is already known, provide a `mean` argument.

```javascript
var accumulator = incrmstdev( 3, 5.0 );
```

#### accumulator( \[x] )

If provided an input value `x`, the accumulator function returns an updated [corrected sample standard deviation][standard-deviation]. If not provided an input value `x`, the accumulator function returns the current [corrected sample standard deviation][standard-deviation].

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

var s = accumulator();
// returns null

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

s = accumulator( 1.0 ); // [2.0, 1.0]
// returns ~0.7071

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

// Window begins sliding...
s = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
// returns ~5.29

s = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
// returns ~5.29

s = accumulator();
// returns ~5.29
```

</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 **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 incrmstdev = require( '@stdlib/stats-incr-mstdev' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrmstdev( 5 );

// For each simulated datum, update the moving corrected sample standard deviation...
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/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/msummary`][@stdlib/stats/incr/msummary]</span><span class="delimiter">: </span><span class="description">compute a moving statistical summary 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>
-   <span class="package-name">[`@stdlib/stats-incr/stdev`][@stdlib/stats/incr/stdev]</span><span class="delimiter">: </span><span class="description">compute a corrected sample standard deviation 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

[![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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[umd]: https://github.com/umdjs/umd
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-mstdev/main/LICENSE

[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation

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

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

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</section>

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