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# incrmvariance

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

<section class="intro">

For a window of size `W`, 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.rawgit.com/stdlib-js/stdlib/27e2a43c70db648bb5bbc3fd0cdee050c25adc0b/lib/node_modules/@stdlib/stats/incr/mvariance/docs/img/equation_unbiased_sample_variance.svg" alt="Equation for the unbiased sample variance.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrmvariance = require( '@stdlib/stats/incr/mvariance' );
```

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

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

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

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

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

#### accumulator( \[x] )

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

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

var s2 = accumulator();
// returns null

// Fill the window...
s2 = accumulator( 2.0 ); // [2.0]
// returns 0.0

s2 = accumulator( 1.0 ); // [2.0, 1.0]
// returns 0.5

s2 = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns 1.0

// Window begins sliding...
s2 = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
// returns 28.0

s2 = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
// returns 28.0

s2 = accumulator();
// returns 28.0
```

</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 incrmvariance = require( '@stdlib/stats/incr/mvariance' );

var accumulator;
var v;
var i;

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

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

</section>

<!-- /.examples -->

<section class="links">

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

</section>

<!-- /.links -->
