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

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# incrmmeanvar

> Compute a moving [arithmetic mean][arithmetic-mean] and [unbiased sample variance][sample-variance] incrementally.

<section class="intro">

For a window of size `W`, the [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" data-equation="eq:arithmetic_mean">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@c8c3c87eeab590bfdff924ec0fb269fb33a7de2b/lib/node_modules/@stdlib/stats/incr/mmeanvar/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
    <br>
</div>

<!-- </equation> -->

and the [unbiased sample variance][sample-variance] is defined as

<!-- <equation class="equation" label="eq:unbiased_sample_variance" align="center" raw="s^2 = \frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2" alt="Equation for the unbiased sample variance."> -->

<div class="equation" align="center" data-raw-text="s^2 = \frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2" data-equation="eq:unbiased_sample_variance">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@563a8587d936008c82db675be84f8ce1474fee27/lib/node_modules/@stdlib/stats/incr/mmeanvar/docs/img/equation_unbiased_sample_variance.svg" alt="Equation for the unbiased sample variance.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrmmeanvar = require( '@stdlib/stats/incr/mmeanvar' );
```

#### incrmmeanvar( \[out,] window )

Returns an accumulator `function` which incrementally computes a moving [arithmetic mean][arithmetic-mean] and [unbiased sample variance][sample-variance]. The `window` parameter defines the number of values over which to compute the moving [arithmetic mean][arithmetic-mean] and [unbiased sample variance][sample-variance].

```javascript
var accumulator = incrmmeanvar( 3 );
```

By default, the returned accumulator `function` returns the accumulated values as a two-element `array`. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var accumulator = incrmmeanvar( new Float64Array( 2 ), 3 );
```

#### accumulator( \[x] )

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

```javascript
var accumulator = incrmmeanvar( 3 );

var out = accumulator();
// returns null

// Fill the window...
out = accumulator( 2.0 ); // [2.0]
// returns [ 2.0, 0.0 ]

out = accumulator( 1.0 ); // [2.0, 1.0]
// returns [ 1.5, 0.5 ]

out = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns [ 2.0, 1.0 ]

// Window begins sliding...
out = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
// returns [ -1.0, 28.0 ]

out = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
// returns [ -3.0, 28.0 ]

out = accumulator();
// returns [ -3.0, 28.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Input values are **not** type checked. If provided `NaN`, the accumulated values are `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` values 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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var Float64Array = require( '@stdlib/array/float64' );
var ArrayBuffer = require( '@stdlib/array/buffer' );
var incrmmeanvar = require( '@stdlib/stats/incr/mmeanvar' );

var offset;
var acc;
var buf;
var out;
var mv;
var N;
var v;
var i;
var j;

// Define the number of accumulators:
N = 5;

// Create an array buffer for storing accumulator output:
buf = new ArrayBuffer( N*2*8 ); // 8 bytes per element

// Initialize accumulators:
acc = [];
for ( i = 0; i < N; i++ ) {
    // Compute the byte offset:
    offset = i * 2 * 8; // stride=2, bytes_per_element=8

    // Create a new view for storing accumulated values:
    out = new Float64Array( buf, offset, 2 );

    // Initialize an accumulator which will write results to the view:
    acc.push( incrmmeanvar( out, 5 ) );
}

// Simulate data and update the moving sample means and variances...
for ( i = 0; i < 100; i++ ) {
    for ( j = 0; j < N; j++ ) {
        v = randu() * 100.0 * (j+1);
        acc[ j ]( v );
    }
}

// Print the final results:
console.log( 'Mean\tVariance' );
for ( i = 0; i < N; i++ ) {
    mv = acc[ i ]();
    console.log( '%d\t%d', mv[ 0 ].toFixed( 3 ), mv[ 1 ].toFixed( 3 ) );
}
```

</section>

<!-- /.examples -->

<section class="links">

[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean

[sample-variance]: https://en.wikipedia.org/wiki/Variance

</section>

<!-- /.links -->