# incrmaape
> Compute the [mean arctangent absolute percentage error][@kim:2016a] (MAAPE) incrementally.
The [mean arctangent absolute percentage error][@kim:2016a] is defined as
where `f_i` is the forecast value and `a_i` is the actual value.
## Usage
```javascript
var incrmaape = require( '@stdlib/stats/incr/maape' );
```
#### incrmaape()
Returns an accumulator `function` which incrementally computes the [mean arctangent absolute percentage error][@kim:2016a].
```javascript
var accumulator = incrmaape();
```
#### accumulator( \[f, a] )
If provided input values `f` and `a`, the accumulator function returns an updated [mean arctangent absolute percentage error][@kim:2016a]. If not provided input values `f` and `a`, the accumulator function returns the current [mean arctangent absolute percentage error][@kim:2016a].
```javascript
var accumulator = incrmaape();
var m = accumulator( 2.0, 3.0 );
// returns ~0.3218
m = accumulator( 1.0, 4.0 );
// returns ~0.4826
m = accumulator( 3.0, 5.0 );
// returns ~0.4486
m = accumulator();
// returns ~0.4486
```
## 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.
- Note that, unlike the [mean absolute percentage error][@stdlib/stats/incr/mape] (MAPE), the [mean arctangent absolute percentage error][@kim:2016a] is expressed in radians on the interval \[0,π/2].
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrmaape = require( '@stdlib/stats/incr/maape' );
var accumulator;
var v1;
var v2;
var i;
// Initialize an accumulator:
accumulator = incrmaape();
// For each simulated datum, update the mean arctangent absolute percentage 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() );
```
## References
- Kim, Sungil, and Heeyoung Kim. 2016. "A new metric of absolute percentage error for intermittent demand forecasts." _International Journal of Forecasting_ 32 (3): 669–79. doi:[10.1016/j.ijforecast.2015.12.003][@kim:2016a].
[@kim:2016a]: https://www.sciencedirect.com/science/article/pii/S0169207016000121
[@stdlib/stats/incr/mape]: https://www.npmjs.com/package/@stdlib/stats/tree/main/incr/mape
