time-to-botec/squiggle/node_modules/@stdlib/stats/incr/mape/README.md

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# 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.jsdelivr.net/gh/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 -->