# incrmvariance
> Compute a moving [unbiased sample variance][sample-variance] incrementally.
For a window of size `W`, the [unbiased sample variance][sample-variance] is defined as
## 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
```
## 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.
## Examples
```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() );
```
[sample-variance]: https://en.wikipedia.org/wiki/Variance
