# incrmpcorrdist

Compute a moving sample Pearson product-moment correlation distance incrementally.

The sample Pearson product-moment correlation distance is defined as

where `r`

is the sample Pearson product-moment correlation coefficient, `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]`

.

## Usage

```
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. The `window`

parameter defines the number of values over which to compute the moving sample Pearson product-moment correlation distance.

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

If means are already known, provide `mx`

and `my`

arguments.

```
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. If not provided input values `x`

and `y`

, the accumulator function returns the current sample Pearson product-moment correlation distance.

```
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
```

## 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 between perfectly correlated random variables may
**not**be`0`

or`2`

. In fact, the sample correlation distance is**not**guaranteed to be strictly on the interval`[0,2]`

. Any computed distance should, however, be within floating-point roundoff error.

## Examples

```
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() );
```