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# incrmmae

> Compute a moving [mean absolute error][mean-absolute-error] (MAE) incrementally.

<section class="intro">

For a window of size `W`, the [mean absolute error][mean-absolute-error] is defined as

<!-- <equation class="equation" label="eq:mean_absolute_error" align="center" raw="\operatorname{MAE} = \frac{1}{W} \sum_{i=0}^{W-1} |y_i - x_i|" alt="Equation for the mean absolute error."> -->

<div class="equation" align="center" data-raw-text="\operatorname{MAE} = \frac{1}{W} \sum_{i=0}^{W-1} |y_i - x_i|" data-equation="eq:mean_absolute_error">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/2fd94e331f96b2984303ca92fad16757cfc5fdcb/lib/node_modules/@stdlib/stats/incr/mmae/docs/img/equation_mean_absolute_error.svg" alt="Equation for the mean absolute error.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrmmae = require( '@stdlib/stats/incr/mmae' );
```

#### incrmmae( window )

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

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

#### accumulator( \[x, y] )

If provided input values `x` and `y`, the accumulator function returns an updated [mean absolute error][mean-absolute-error]. If not provided input values `x` and `y`, the accumulator function returns the current [mean absolute error][mean-absolute-error].

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

var m = accumulator();
// returns null

// Fill the window...
m = accumulator( 2.0, 3.0 ); // [(2.0,3.0)]
// returns 1.0

m = accumulator( -1.0, 4.0 ); // [(2.0,3.0), (-1.0,4.0)]
// returns 3.0

m = accumulator( 3.0, 9.0 ); // [(2.0,3.0), (-1.0,4.0), (3.0,9.0)]
// returns 4.0

// Window begins sliding...
m = accumulator( -7.0, 3.0 ); // [(-1.0,4.0), (3.0,9.0), (-7.0,3.0)]
// returns 7.0

m = accumulator( -5.0, -3.0 ); // [(3.0,9.0), (-7.0,3.0), (-5.0,-3.0)]
// returns 6.0

m = accumulator();
// returns 6.0
```

</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` (x,y) pairs 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.
-   **Warning**: the [mean absolute error][mean-absolute-error] is scale-dependent and, thus, the measure should **not** be used to make comparisons between datasets having different scales.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrmmae = require( '@stdlib/stats/incr/mmae' );

var accumulator;
var v1;
var v2;
var i;

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

// For each simulated datum, update the moving mean absolute error...
for ( i = 0; i < 100; i++ ) {
    v1 = ( randu()*100.0 ) - 50.0;
    v2 = ( randu()*100.0 ) - 50.0;
    accumulator( v1, v2 );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<section class="links">

[mean-absolute-error]: https://en.wikipedia.org/wiki/Mean_absolute_error

</section>

<!-- /.links -->
