feat: add incremental exponentially weighted standard deviation accumulator

Author: Girish-Garg

lib/node_modules/@stdlib/stats/incr/nanewstdev/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2018 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# incrnanewstdev
+
+> Compute an [exponentially weighted standard deviation][moving-average] incrementally.
+
+<section class="intro">
+
+An [exponentially weighted variance][moving-average] can be defined recursively as
+
+<!-- <equation class="equation" label="eq:exponentially_weighted_variance" align="center" raw="S_n = \begin{cases} 0 & \textrm{if}\ n = 0 \\ (1 - \alpha) (S_{n-1} + \alpha(x_n - \mu_{n-1})^2) & \textrm{if}\ n > 0 \end{cases}" alt="Recursive definition for computing an exponentially weighted variance."> -->
+
+```math
+S_n = \begin{cases} 0 & \textrm{if}\ n = 0 \\ (1 - \alpha) (S_{n-1} + \alpha(x_n - \mu_{n-1})^2) & \textrm{if}\ n > 0 \end{cases}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="S_n = \begin{cases} 0 &amp; \textrm{if}\ n = 0 \\ (1 - \alpha) (S_{n-1} + \alpha(x_n - \mu_{n-1})^2) &amp; \textrm{if}\ n &gt; 0 \end{cases}" data-equation="eq:exponentially_weighted_variance">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@b6bfc5be3086b5ddfeed2311afee7c9201fbdcbb/lib/node_modules/@stdlib/stats/incr/nanewstdev/docs/img/equation_exponentially_weighted_variance.svg" alt="Recursive definition for computing an exponentially weighted variance.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `μ` is the [exponentially weighted mean][@stdlib/stats/incr/ewmean]. The [exponentially weighted standard deviation][moving-average] is the square root of the [exponentially weighted variance][moving-average].
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var incrnanewstdev = require( '@stdlib/stats/incr/nanewstdev' );
+```
+
+#### incrnanewstdev( alpha )
+
+Returns an accumulator `function` which incrementally computes an [exponentially weighted standard deviation][moving-average], where `alpha` is a smoothing factor between `0` and `1`.
+
+```javascript
+var accumulator = incrnanewstdev( 0.5 );
+```
+
+#### accumulator( \[x] )
+
+If provided an input value `x`, the accumulator function returns an updated standard deviation. If not provided an input value `x`, the accumulator function returns the current standard deviation.
+
+```javascript
+var accumulator = incrnanewstdev( 0.5 );
+
+var s = accumulator();
+// returns null
+
+s = accumulator( 2.0 );
+// returns 0.0
+
+s = accumulator( 1.0 );
+// returns 0.5
+
+s = accumulator( NaN );
+// returns 0.5
+
+s = accumulator( 3.0 );
+// returns ~0.83
+
+s = accumulator();
+// returns ~0.83
+```
+
+</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`, it will be **ignored** but you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var incrnanewstdev = require( './../lib' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+
+var accumulator;
+var s;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanewstdev( 0.5 );
+
+// For each simulated datum, update the exponentially weighted standard deviation...
+for ( i = 0; i < 100; i++ ) {
+    v = (randu() < 0.1) ? NaN : randu() * 100.0;
+    s = accumulator( v );
+}
+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/ewvariance`][@stdlib/stats/incr/ewvariance]</span><span class="delimiter">: </span><span class="description">compute an exponentially weighted variance incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/mstdev`][@stdlib/stats/incr/mstdev]</span><span class="delimiter">: </span><span class="description">compute a moving corrected sample standard deviation incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/stdev`][@stdlib/stats/incr/stdev]</span><span class="delimiter">: </span><span class="description">compute a corrected sample standard deviation incrementally.</span>
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[moving-average]: https://en.wikipedia.org/wiki/Moving_average
+
+[@stdlib/stats/incr/ewmean]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/ewmean
+
+<!-- <related-links> -->
+
+[@stdlib/stats/incr/ewvariance]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/ewvariance
+
+[@stdlib/stats/incr/mstdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mstdev
+
+[@stdlib/stats/incr/stdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/stdev
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var pkg = require( './../package.json' ).name;
+var incrnanewstdev = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = incrnanewstdev( 0.5 );
+		if ( typeof f !== 'function' ) {
+			b.fail( 'should return a function' );
+		}
+	}
+	b.toc();
+	if ( typeof f !== 'function' ) {
+		b.fail( 'should return a function' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::accumulator', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+
+	acc = incrnanewstdev( 0.5 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu() );
+		if ( v !== v ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( v !== v ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});