# incrmmeanvar
> Compute a moving [arithmetic mean][arithmetic-mean] and [unbiased sample variance][sample-variance] incrementally.
For a window of size `W`, the [arithmetic mean][arithmetic-mean] is defined as
and the [unbiased sample variance][sample-variance] is defined as
## Usage
```javascript
var incrmmeanvar = require( '@stdlib/stats/incr/mmeanvar' );
```
#### incrmmeanvar( \[out,] window )
Returns an accumulator `function` which incrementally computes a moving [arithmetic mean][arithmetic-mean] and [unbiased sample variance][sample-variance]. The `window` parameter defines the number of values over which to compute the moving [arithmetic mean][arithmetic-mean] and [unbiased sample variance][sample-variance].
```javascript
var accumulator = incrmmeanvar( 3 );
```
By default, the returned accumulator `function` returns the accumulated values as a two-element `array`. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var accumulator = incrmmeanvar( new Float64Array( 2 ), 3 );
```
#### accumulator( \[x] )
If provided an input value `x`, the accumulator function returns updated accumulated values. If not provided an input value `x`, the accumulator function returns the current accumulated values.
```javascript
var accumulator = incrmmeanvar( 3 );
var out = accumulator();
// returns null
// Fill the window...
out = accumulator( 2.0 ); // [2.0]
// returns [ 2.0, 0.0 ]
out = accumulator( 1.0 ); // [2.0, 1.0]
// returns [ 1.5, 0.5 ]
out = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns [ 2.0, 1.0 ]
// Window begins sliding...
out = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
// returns [ -1.0, 28.0 ]
out = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
// returns [ -3.0, 28.0 ]
out = accumulator();
// returns [ -3.0, 28.0 ]
```
## Notes
- Input values are **not** type checked. If provided `NaN`, the accumulated values are `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 Float64Array = require( '@stdlib/array/float64' );
var ArrayBuffer = require( '@stdlib/array/buffer' );
var incrmmeanvar = require( '@stdlib/stats/incr/mmeanvar' );
var offset;
var acc;
var buf;
var out;
var mv;
var N;
var v;
var i;
var j;
// Define the number of accumulators:
N = 5;
// Create an array buffer for storing accumulator output:
buf = new ArrayBuffer( N*2*8 ); // 8 bytes per element
// Initialize accumulators:
acc = [];
for ( i = 0; i < N; i++ ) {
// Compute the byte offset:
offset = i * 2 * 8; // stride=2, bytes_per_element=8
// Create a new view for storing accumulated values:
out = new Float64Array( buf, offset, 2 );
// Initialize an accumulator which will write results to the view:
acc.push( incrmmeanvar( out, 5 ) );
}
// Simulate data and update the moving sample means and variances...
for ( i = 0; i < 100; i++ ) {
for ( j = 0; j < N; j++ ) {
v = randu() * 100.0 * (j+1);
acc[ j ]( v );
}
}
// Print the final results:
console.log( 'Mean\tVariance' );
for ( i = 0; i < N; i++ ) {
mv = acc[ i ]();
console.log( '%d\t%d', mv[ 0 ].toFixed( 3 ), mv[ 1 ].toFixed( 3 ) );
}
```
[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
[sample-variance]: https://en.wikipedia.org/wiki/Variance
