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# incrmpe

> Compute the [mean percentage error][mean-percentage-error] (MPE) incrementally.

<section class="intro">

The [mean percentage error][mean-percentage-error] is defined as

<!-- <equation class="equation" label="eq:mean_percentage_error" align="center" raw="\operatorname{MPE}  = \frac{100}{n} \sum_{i=0}^{n-1} \frac{a_i - f_i}{a_i}" alt="Equation for the mean percentage error."> -->

<div class="equation" align="center" data-raw-text="\operatorname{MPE}  = \frac{100}{n} \sum_{i=0}^{n-1} \frac{a_i - f_i}{a_i}" data-equation="eq:mean_percentage_error">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/2acedf866c9a4f1353af22f95780535612c5ee06/lib/node_modules/@stdlib/stats/incr/mpe/docs/img/equation_mean_percentage_error.svg" alt="Equation for the mean percentage error.">
    <br>
</div>

<!-- </equation> -->

where `f_i` is the forecast value and `a_i` is the actual value.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrmpe = require( '@stdlib/stats/incr/mpe' );
```

#### incrmpe()

Returns an accumulator `function` which incrementally computes the [mean percentage error][mean-percentage-error].

```javascript
var accumulator = incrmpe();
```

#### 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 = incrmpe();

var m = accumulator( 2.0, 3.0 );
// returns ~33.33

m = accumulator( 1.0, 4.0 );
// returns ~54.17

m = accumulator( 3.0, 5.0 );
// returns ~49.44

m = accumulator();
// returns ~49.44
```

</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 **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.
-   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). 

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

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

// Initialize an accumulator:
accumulator = incrmpe();

// For each simulated datum, update the 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() );
```

</section>

<!-- /.examples -->

<section class="links">

[mean-percentage-error]: https://en.wikipedia.org/wiki/Mean_percentage_error

</section>

<!-- /.links -->
