# increwvariance
> Compute an [exponentially weighted variance][moving-average] incrementally.
An [exponentially weighted variance][moving-average] can be defined recursively as
where `μ` is the [exponentially weighted mean][@stdlib/stats/incr/ewmean].
## 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
```
## 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.
## Examples
```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() );
```
[moving-average]: https://en.wikipedia.org/wiki/Moving_average
[@stdlib/stats/incr/ewmean]: https://www.npmjs.com/package/@stdlib/stats/tree/main/incr/ewmean
