time-to-botec/squiggle/node_modules/@stdlib/stats/incr/mstdev/README.md

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# incrmstdev

> 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="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 class="links">

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

</section>

<!-- /.links -->