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# increwmean

> Compute an [exponentially weighted mean][moving-average] incrementally.

<section class="intro">

An [exponentially weighted mean][moving-average] can be defined recursively as

<!-- <equation class="equation" label="eq:exponentially_weighted_mean" align="center" raw="\mu_t = \begin{cases} x_0 & \textrm{if}\ t = 0 \\ \alpha x_t + (1-\alpha) \mu_{t-1} & \textrm{if}\ t > 0 \end{cases}" alt="Recursive definition for computing an exponentially weighted mean."> -->

<div class="equation" align="center" data-raw-text="\mu_t = \begin{cases} x_0 &amp; \textrm{if}\ t = 0 \\ \alpha x_t + (1-\alpha) \mu_{t-1} &amp; \textrm{if}\ t &gt; 0 \end{cases}" data-equation="eq:exponentially_weighted_mean">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/1445ad5c454bc3c1a86bde2be87d6cec87781174/lib/node_modules/@stdlib/stats/incr/ewmean/docs/img/equation_exponentially_weighted_mean.svg" alt="Recursive definition for computing an exponentially weighted mean.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var increwmean = require( '@stdlib/stats/incr/ewmean' );
```

#### increwmean( alpha )

Returns an accumulator `function` which incrementally computes an [exponentially weighted mean][moving-average], where `alpha` is a smoothing factor between `0` and `1`.

```javascript
var accumulator = increwmean( 0.5 );
```

#### accumulator( \[x] )

If provided an input value `x`, the accumulator function returns an updated mean. If not provided an input value `x`, the accumulator function returns the current mean.

```javascript
var accumulator = increwmean( 0.5 );

var v = accumulator();
// returns null

v = accumulator( 2.0 );
// returns 2.0

v = accumulator( 1.0 );
// returns 1.5

v = accumulator( 3.0 );
// returns 2.25

v = accumulator();
// returns 2.25
```

</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 increwmean = require( '@stdlib/stats/incr/ewmean' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = increwmean( 0.5 );

// For each simulated datum, update the exponentially weighted mean...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<section class="links">

[moving-average]: https://en.wikipedia.org/wiki/Moving_average

</section>

<!-- /.links -->
