time-to-botec

README.md (5793B)

---

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 # incrmpcorr
 
 > Compute a moving [sample Pearson product-moment correlation coefficient][pearson-correlation] incrementally.
 
 <section class="intro">
 
 The [Pearson product-moment correlation coefficient][pearson-correlation] between random variables `X` and `Y` is defined as
 
 <!-- <equation class="equation" label="eq:pearson_correlation_coefficient" align="center" raw="\rho_{X,Y} = \frac{\operatorname{cov}(X,Y)}{\sigma_X \sigma_Y}" alt="Equation for the Pearson product-moment correlation coefficient."> -->
 
 <div class="equation" align="center" data-raw-text="\rho_{X,Y} = \frac{\operatorname{cov}(X,Y)}{\sigma_X \sigma_Y}" data-equation="eq:pearson_correlation_coefficient">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/mpcorr/docs/img/equation_pearson_correlation_coefficient.svg" alt="Equation for the Pearson product-moment correlation coefficient.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 where the numerator is the [covariance][covariance] and the denominator is the product of the respective standard deviations.
 
 For a sample of size `W`, the [sample Pearson product-moment correlation coefficient][pearson-correlation] is defined as
 
 <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
 
 <div class="equation" align="center" data-raw-text="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/mpcorr/docs/img/equation_sample_pearson_correlation_coefficient.svg" alt="Equation for the sample Pearson product-moment correlation coefficient.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 </section>
 
 <!-- /.intro -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var incrmpcorr = require( '@stdlib/stats/incr/mpcorr' );
 ```
 
 #### incrmpcorr( window\[, mx, my] )
 
 Returns an accumulator `function` which incrementally computes a moving [sample Pearson product-moment correlation coefficient][pearson-correlation]. The `window` parameter defines the number of values over which to compute the moving [sample Pearson product-moment correlation coefficient][pearson-correlation].
 
 ```javascript
 var accumulator = incrmpcorr( 3 );
 ```
 
 If means are already known, provide `mx` and `my` arguments.
 
 ```javascript
 var accumulator = incrmpcorr( 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 coefficient][pearson-correlation]. If not provided input values `x` and `y`, the accumulator function returns the current [sample Pearson product-moment correlation coefficient][pearson-correlation].
 
 ```javascript
 var accumulator = incrmpcorr( 3 );
 
 var r = accumulator();
 // returns null
 
 // Fill the window...
 r = accumulator( 2.0, 1.0 ); // [(2.0, 1.0)]
 // returns 0.0
 
 r = accumulator( -5.0, 3.14 ); // [(2.0, 1.0), (-5.0, 3.14)]
 // returns ~-1.0
 
 r = accumulator( 3.0, -1.0 ); // [(2.0, 1.0), (-5.0, 3.14), (3.0, -1.0)]
 // returns ~-0.925
 
 // Window begins sliding...
 r = accumulator( 5.0, -9.5 ); // [(-5.0, 3.14), (3.0, -1.0), (5.0, -9.5)]
 // returns ~-0.863
 
 r = accumulator( -5.0, 1.5 ); // [(3.0, -1.0), (5.0, -9.5), (-5.0, 1.5)]
 // returns ~-0.803
 
 r = accumulator();
 // returns ~-0.803
 ```
 
 </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.
 
 </section>
 
 <!-- /.notes -->
 
 <section class="examples">
 
 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var randu = require( '@stdlib/random/base/randu' );
 var incrmpcorr = require( '@stdlib/stats/incr/mpcorr' );
 
 var accumulator;
 var x;
 var y;
 var i;
 
 // Initialize an accumulator:
 accumulator = incrmpcorr( 5 );
 
 // For each simulated datum, update the moving sample correlation coefficient...
 for ( i = 0; i < 100; i++ ) {
     x = randu() * 100.0;
     y = randu() * 100.0;
     accumulator( x, y );
 }
 console.log( accumulator() );
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <section class="links">
 
 [pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
 
 [covariance]: https://en.wikipedia.org/wiki/Covariance
 
 </section>
 
 <!-- /.links -->