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feat: add stats/incr/nanmvariance
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‎lib/node_modules/@stdlib/stats/incr/nanmvariance/README.md

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# nanmvariance
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> Compute a moving [unbiased sample variance][sample-variance] incrementally, ignoring `NaN` values.
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<section class="intro">
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For a window of size `W`, the [unbiased sample variance][sample-variance] is defined as
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<!-- <equation class="equation" label="eq:unbiased_sample_variance" align="center" raw="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2" alt="Equation for the unbiased sample variance."> -->
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```math
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s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2
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```
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<!-- <div class="equation" align="center" data-raw-text="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2" data-equation="eq:unbiased_sample_variance">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/mvariance/docs/img/equation_unbiased_sample_variance.svg" alt="Equation for the unbiased sample variance.">
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<br>
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</div> -->
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<!-- </equation> -->
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where `n` is the number of non-`NaN` values in the window, and `\bar{x}` is the arithmetic mean of the non-`NaN` values.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var incrnanmvariance = require( '@stdlib/stats/incr/nanmvariance' );
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```
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#### incrnanmvariance( window\[, mean] )
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Returns an accumulator `function` which incrementally computes a moving [unbiased sample variance][sample-variance], ignoring `NaN` values. The `window` parameter defines the number of values over which to compute the moving [unbiased sample variance][sample-variance].
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```javascript
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var accumulator = incrnanmvariance( 3 );
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```
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If the mean is already known, provide a `mean` argument.
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```javascript
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var accumulator = incrnanmvariance( 3, 5.0 );
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```
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#### accumulator( \[x] )
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If provided an input value `x`, the accumulator function returns an updated [unbiased sample variance][sample-variance]. If not provided an input value `x`, the accumulator function returns the current [unbiased sample variance][sample-variance].
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```javascript
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var accumulator = incrnanmvariance( 3 );
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var s2 = accumulator();
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// returns null
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// Fill the window...
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s2 = accumulator( 2.0 ); // [2.0]
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// returns 0.0
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s2 = accumulator( NaN ); // [2.0, NaN]
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// returns 0.0
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s2 = accumulator( -5.0 ); // [2.0, NaN, -5.0]
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// returns 24.5
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// Window begins sliding...
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s2 = accumulator( 3.0 ); // [NaN, -5.0, 3.0]
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// returns 32.0
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s2 = accumulator( NaN ); // [-5.0, 3.0, NaN]
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// returns 32.0
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s2 = accumulator();
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// returns 32.0
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- Input values are **not** type checked. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
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- NaN input values are ignored. If the window contains only NaN values, the variance is calculated as if the window were empty.
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- 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 non-NaN values.
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- The implementation uses [Welford's algorithm][welford-algorithm].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var randu = require( '@stdlib/random/base/randu' );
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var incrnanmvariance = require( '@stdlib/stats/incr/nanmvariance' );
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var accumulator;
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var v;
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var i;
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// Initialize an accumulator:
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accumulator = incrnanmvariance( 5 );
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// For each simulated datum, update the moving unbiased sample variance...
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console.log( '\nValue\tSample Variance\n' );
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for ( i = 0; i < 100; i++ ) {
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if ( randu() < 0.2 ) {
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v = NaN;
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} else {
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v = randu() * 100.0;
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}
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console.log( '%d\t%d', v.toFixed( 4 ), accumulator( v ).toFixed( 4 ) );
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}
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console.log( '\nFinal variance: %d\n', accumulator() );
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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* * *
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## See Also
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- <span class="package-name">[`@stdlib/stats/incr/mvariance`][@stdlib/stats/incr/mvariance]</span><span class="delimiter">: </span><span class="description">compute a moving unbiased sample variance incrementally.</span>
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- <span class="package-name">[`@stdlib/stats/incr/nanmmean`][@stdlib/stats/incr/nanmmean]</span><span class="delimiter">: </span><span class="description">compute a moving arithmetic mean incrementally, ignoring NaN values.</span>
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- <span class="package-name">[`@stdlib/stats/incr/nanmstdev`][@stdlib/stats/incr/nanmstdev]</span><span class="delimiter">: </span><span class="description">compute a moving corrected sample standard deviation incrementally, ignoring NaN values.</span>
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- <span class="package-name">[`@stdlib/stats/incr/nanvariance`][@stdlib/stats/incr/nanvariance]</span><span class="delimiter">: </span><span class="description">compute an unbiased sample variance incrementally, ignoring NaN values.</span>
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[sample-variance]: https://en.wikipedia.org/wiki/Variance
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[welford-algorithm]: https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm
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<!-- <related-links> -->
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[@stdlib/stats/incr/mvariance]: https://github.com/stdlib-js/stats-incr-mvariance
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[@stdlib/stats/incr/nanmmean]: https://github.com/stdlib-js/stats-incr-nanmmean
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[@stdlib/stats/incr/nanmstdev]: https://github.com/stdlib-js/stats-incr-nanmstdev
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[@stdlib/stats/incr/nanvariance]: https://github.com/stdlib-js/stats-incr-nanvariance
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/incr/nanmvariance/benchmark/benchmark.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var randu = require( '@stdlib/random/base/randu' );
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var pkg = require( './../package.json' ).name;
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var incrnanmvariance = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var f;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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f = incrnanmvariance( (i%5)+1 );
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if ( typeof f !== 'function' ) {
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b.fail( 'should return a function' );
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}
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}
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b.toc();
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if ( typeof f !== 'function' ) {
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b.fail( 'should return a function' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::accumulator', function benchmark( b ) {
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var acc;
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var v;
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var i;
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acc = incrnanmvariance( 5 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = acc( randu() );
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::accumulator,NaN', function benchmark( b ) {
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var acc;
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var v;
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var i;
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acc = incrnanmvariance( 5 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = acc( NaN );
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::accumulator,known_mean', function benchmark( b ) {
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var acc;
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var v;
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var i;
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acc = incrnanmvariance( 5, 0.5 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = acc( randu() );
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( v !== v ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

‎lib/node_modules/@stdlib/stats/incr/nanmvariance/docs/img/equation_unbiased_sample_variance.svg

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‎lib/node_modules/@stdlib/stats/incr/nanmvariance/docs/repl.txt

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{{alias}}( W[, mean] )
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Returns an accumulator function which incrementally computes a moving
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unbiased sample variance, ignoring NaN values.
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The `W` parameter defines the number of values over which to compute the
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moving unbiased sample variance.
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If provided a value, the accumulator function returns an updated moving
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unbiased sample variance. If not provided a value, the accumulator function
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returns the current moving unbiased sample variance.
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NaN input values are ignored. If the window contains only NaN values, the
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variance is calculated as if the window were empty.
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As `W` values are needed to fill the window buffer, the first `W-1` returned
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values are calculated from smaller sample sizes. Until the window is full,
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each returned value is calculated from all provided non-NaN values.
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Parameters
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----------
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W: integer
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Window size.
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mean: number (optional)
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Known mean.
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Returns
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-------
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acc: Function
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Accumulator function.
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Examples
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--------
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> var accumulator = {{alias}}( 3 );
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> var s2 = accumulator()
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null
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> s2 = accumulator( 2.0 )
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0.0
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> s2 = accumulator( NaN )
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0.0
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> s2 = accumulator( -5.0 )
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24.5
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> s2 = accumulator( 3.0 )
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19.0
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> s2 = accumulator( NaN )
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19.0
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> s2 = accumulator()
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19.0
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See Also
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--------

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