@stdlib/stats/incr/mpcorrdist/README.md

Standard library statistical functions.

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# incrmpcorrdist

> Compute a moving [sample Pearson product-moment correlation distance][pearson-correlation] incrementally.

<section class="intro">

The [sample Pearson product-moment correlation distance][pearson-correlation] is defined as

<!-- <equation class="equation" label="eq:pearson_distance" align="center" raw="d_{x,y} = 1 - r_{x,y} = 1 - \frac{\operatorname{cov_n(x,y)}}{\sigma_x \sigma_y}" alt="Equation for the Pearson product-moment correlation distance."> -->

<div class="equation" align="center" data-raw-text="d_{x,y} = 1 - r_{x,y} = 1 - \frac{\operatorname{cov_n(x,y)}}{\sigma_x \sigma_y}" data-equation="eq:pearson_distance">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/mpcorrdist/docs/img/equation_pearson_distance.svg" alt="Equation for the Pearson product-moment correlation distance.">
    <br>
</div>

<!-- </equation> -->

where `r` is the [sample Pearson product-moment correlation coefficient][pearson-correlation], `cov(x,y)` is the sample covariance, and `σ` corresponds to the sample standard deviation. As `r` resides on the interval `[-1,1]`, `d` resides on the interval `[0,2]`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrmpcorrdist = require( '@stdlib/stats/incr/mpcorrdist' );
```

#### incrmpcorrdist( window\[, mx, my] )

Returns an accumulator `function` which incrementally computes a moving [sample Pearson product-moment correlation distance][pearson-correlation]. The `window` parameter defines the number of values over which to compute the moving [sample Pearson product-moment correlation distance][pearson-correlation].

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

If means are already known, provide `mx` and `my` arguments.

```javascript
var accumulator = incrmpcorrdist( 3, 5.0, -3.14 );
```

#### accumulator( \[x, y] )

If provided input values `x` and `y`, the accumulator function returns an updated [sample Pearson product-moment correlation distance][pearson-correlation]. If not provided input values `x` and `y`, the accumulator function returns the current [sample Pearson product-moment correlation distance][pearson-correlation].

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

var r = accumulator();
// returns null

// Fill the window...
r = accumulator( 2.0, 1.0 ); // [(2.0, 1.0)]
// returns 1.0

r = accumulator( -5.0, 3.14 ); // [(2.0, 1.0), (-5.0, 3.14)]
// returns ~2.0

r = accumulator( 3.0, -1.0 ); // [(2.0, 1.0), (-5.0, 3.14), (3.0, -1.0)]
// returns ~1.925

// Window begins sliding...
r = accumulator( 5.0, -9.5 ); // [(-5.0, 3.14), (3.0, -1.0), (5.0, -9.5)]
// returns ~1.863

r = accumulator( -5.0, 1.5 ); // [(3.0, -1.0), (5.0, -9.5), (-5.0, 1.5)]
// returns ~1.803

r = accumulator();
// returns ~1.803
```

</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 **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` (x,y) pairs 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.
-   Due to limitations inherent in representing numeric values using floating-point format (i.e., the inability to represent numeric values with infinite precision), the [sample correlation distance][pearson-correlation] between perfectly correlated random variables may **not** be `0` or `2`. In fact, the [sample correlation distance][pearson-correlation] is **not** guaranteed to be strictly on the interval `[0,2]`. Any computed distance should, however, be within floating-point roundoff error.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

var accumulator;
var x;
var y;
var i;

// Initialize an accumulator:
accumulator = incrmpcorrdist( 5 );

// For each simulated datum, update the moving sample correlation distance...
for ( i = 0; i < 100; i++ ) {
    x = randu() * 100.0;
    y = randu() * 100.0;
    accumulator( x, y );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/stats/incr/mpcorr`][@stdlib/stats/incr/mpcorr]</span><span class="delimiter">: </span><span class="description">compute a moving sample Pearson product-moment correlation coefficient incrementally.</span>
-   <span class="package-name">[`@stdlib/stats/incr/pcorrdist`][@stdlib/stats/incr/pcorrdist]</span><span class="delimiter">: </span><span class="description">compute a sample Pearson product-moment correlation distance.</span>

</section>

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<section class="links">

[pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

<!-- <related-links> -->

[@stdlib/stats/incr/mpcorr]: https://github.com/stdlib-js/stats/tree/main/incr/mpcorr

[@stdlib/stats/incr/pcorrdist]: https://github.com/stdlib-js/stats/tree/main/incr/pcorrdist

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</section>

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