<!--

@license Apache-2.0

Copyright (c) 2018 The Stdlib Authors.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

   http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

-->

# incrmape

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

<section class="intro">

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

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

<div class="equation" align="center" data-raw-text="\operatorname{MAPE}  = \frac{100}{n} \sum_{i=0}^{n-1} \biggl| \frac{a_i - f_i}{a_i} \biggr|" data-equation="eq:mean_absolute_percentage_error">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/d4867162fd6445b10f93ca01f3f764bc646662d8/lib/node_modules/@stdlib/stats/incr/mape/docs/img/equation_mean_absolute_percentage_error.svg" alt="Equation for the mean absolute 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 incrmape = require( '@stdlib/stats/incr/mape' );
```

#### incrmape()

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

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

#### accumulator( \[f, a] )

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

```javascript
var accumulator = incrmape();

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.

-   **Warning**: the [mean absolute percentage error][mean-absolute-percentage-error]  has several shortcomings: 

    -   The measure is **not** suitable for intermittent demand patterns (i.e., when `a_i` is `0`).
    -   The [mean absolute percentage error][mean-absolute-percentage-error] is not symmetrical, as the measure cannot exceed 100% for forecasts which are too "low" and has no limit for forecasts which are too "high".
    -   When used to compare the accuracy of forecast models (e.g., predicting demand), the measure is biased toward forecasts which are too low. 

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

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

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

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

</section>

<!-- /.examples -->

<section class="links">

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

</section>

<!-- /.links -->
