npm package: @stdlib/stats-incr-mmpe
Description: Compute a moving mean percentage error (MPE) incrementally.
Author: The Stdlib Authors
Latest version: 0.2.3

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# incrmmpe

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

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

<section class="intro">

For a window of size `W`, 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}{W} \sum_{i=0}^{W-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}{W} \sum_{i=0}^{W-1} \frac{a_i - f_i}{a_i}" data-equation="eq:mean_percentage_error">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d97022bce00ceb9db681cb6cc8fb6c87ad86287f/lib/node_modules/@stdlib/stats/incr/mmpe/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="installation">

## Installation

```bash
npm install @stdlib/stats-incr-mmpe
```

</section>

<section class="usage">

## 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
```

</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` (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).

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```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() );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/stats-incr/mmape`][@stdlib/stats/incr/mmape]</span><span class="delimiter">: </span><span class="description">compute a moving mean absolute percentage error (MAPE) incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/mme`][@stdlib/stats/incr/mme]</span><span class="delimiter">: </span><span class="description">compute a moving mean error (ME) incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/mpe`][@stdlib/stats/incr/mpe]</span><span class="delimiter">: </span><span class="description">compute the mean percentage error (MPE) incrementally.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[umd]: https://github.com/umdjs/umd
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[mean-percentage-error]: https://en.wikipedia.org/wiki/Mean_percentage_error

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