# incrmmpe
> Compute a moving [mean percentage error][mean-percentage-error] (MPE) incrementally.
For a window of size `W`, the [mean percentage error][mean-percentage-error] is defined as
where `f_i` is the forecast value and `a_i` is the actual value.
## Usage
```javascript
var incrmmpe = require( '@stdlib/stats/incr/mmpe' );
```
#### incrmmpe( window )
Returns an accumulator `function` which incrementally computes a moving [mean percentage error][mean-percentage-error]. The `window` parameter defines the number of values over which to compute the moving [mean percentage error][mean-percentage-error].
```javascript
var accumulator = incrmmpe( 3 );
```
#### accumulator( \[f, a] )
If provided input values `f` and `a`, the accumulator function returns an updated [mean percentage error][mean-percentage-error]. If not provided input values `f` and `a`, the accumulator function returns the current [mean percentage error][mean-percentage-error].
```javascript
var accumulator = incrmmpe( 3 );
var m = accumulator();
// returns null
// Fill the window...
m = accumulator( 2.0, 3.0 ); // [(2.0,3.0)]
// returns ~33.33
m = accumulator( 1.0, 4.0 ); // [(2.0,3.0), (1.0,4.0)]
// returns ~54.17
m = accumulator( 3.0, 9.0 ); // [(2.0,3.0), (1.0,4.0), (3.0,9.0)]
// returns ~58.33
// Window begins sliding...
m = accumulator( 7.0, 3.0 ); // [(1.0,4.0), (3.0,9.0), (7.0,3.0)]
// returns ~2.78
m = accumulator( 5.0, 3.0 ); // [(3.0,9.0), (7.0,3.0), (5.0,3.0)]
// returns ~-44.44
m = accumulator();
// returns ~-44.44
```
## 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` (f,a) 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.
- Be careful when interpreting the [mean percentage error][mean-percentage-error] as errors can cancel. This stated, that errors can cancel makes the [mean percentage error][mean-percentage-error] suitable for measuring the bias in forecasts.
- **Warning**: the [mean percentage error][mean-percentage-error] is **not** suitable for intermittent demand patterns (i.e., when `a_i` is `0`). Interpretation is most straightforward when actual and forecast values are positive valued (e.g., number of widgets sold).
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrmmpe = require( '@stdlib/stats/incr/mmpe' );
var accumulator;
var v1;
var v2;
var i;
// Initialize an accumulator:
accumulator = incrmmpe( 5 );
// For each simulated datum, update the moving mean 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() );
```
[mean-percentage-error]: https://en.wikipedia.org/wiki/Mean_percentage_error
