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# incrmda

> Compute the [mean directional accuracy][mean-directional-accuracy] (MDA) incrementally.

<section class="intro">

The [mean directional accuracy][mean-directional-accuracy] is defined as

<!-- <equation class="equation" label="eq:mean_directional_accuracy" align="center" raw="\operatorname{MDA} = \begin{cases} 1 & \textrm{if}\ N = 1 \\\frac{1}{N} \sum_{i=1}^{N} \delta_{\operatorname{sgn}(\Delta f_{i,i-1}),\ \operatorname{sgn}(\Delta a_{i,i-1})} & \textrm{if}\ N > 1 \end{cases}" alt="Equation for the mean directional accuracy."> -->

<div class="equation" align="center" data-raw-text="\operatorname{MDA} = \begin{cases} 1 & \textrm{if}\ N = 1 \\\frac{1}{N} \sum_{i=1}^{N} \delta_{\operatorname{sgn}(\Delta f_{i,i-1}),\ \operatorname{sgn}(\Delta a_{i,i-1})} & \textrm{if}\ N > 1 \end{cases}" data-equation="eq:mean_directional_accuracy">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/95b364439921fe28429acff89c5ba464a5a60caf/lib/node_modules/@stdlib/stats/incr/mda/docs/img/equation_mean_directional_accuracy.svg" alt="Equation for the mean directional accuracy.">
    <br>
</div>

<!-- </equation> -->

where `f_i` is the forecast value, `a_i` is the actual value, `sgn(x)` is the [signum][@stdlib/math/base/special/signum] function, and `δ` is the [Kronecker delta][@stdlib/math/base/special/kronecker-delta]. 

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrmda = require( '@stdlib/stats/incr/mda' );
```

#### incrmda()

Returns an accumulator `function` which incrementally computes the [mean directional accuracy][mean-directional-accuracy].

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

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

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

```javascript
var accumulator = incrmda();

var m = accumulator( 2.0, 3.0 );
// returns 1.0

m = accumulator( -1.0, 4.0 );
// returns 0.5

m = accumulator( -3.0, -2.0 );
// returns ~0.67

m = accumulator();
// returns ~0.67
```

</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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

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

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

// For each simulated datum, update the mean directional accuracy...
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-directional-accuracy]: https://en.wikipedia.org/wiki/Mean_Directional_Accuracy_%28MDA%29

[@stdlib/math/base/special/signum]: https://github.com/stdlib-js/math-base-special-signum

[@stdlib/math/base/special/kronecker-delta]: https://github.com/stdlib-js/math-base-special-kronecker-delta

</section>

<!-- /.links -->
