feat(stats/incr): add nanewvariance module

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# nanewvariance
+
+> Compute an [exponentially weighted variance][exponentially weighted variance] incrementally, ignoring `NaN` values.
+
+<section class="intro">
+
+The [exponentially weighted variance][exponentially weighted variance] is defined as
+
+<!-- <equation class="equation" label="eq:ew_variance" align="center" raw="s_t^2 = (1-\alpha) \left( s_{t-1}^2 + \alpha (x_t - \mu_{t-1})^2 \right)" alt="Equation for the 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="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:exponentially weighted variance">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/nanmean/docs/img/equation_exponentially_weighted_variance.svg" alt="exponentially weighted variance">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var nanewvariance = require( '@stdlib/stats/incr/nanewvariance' );
+```
+
+#### nanewvariance()
+
+Returns an accumulator function which incrementally computes an [exponentially weighted variance][exponentially weighted variance], ignoring `NaN` values.
+
+```javascript
+var accumulator = nanewvariance( 0.5 );
+```
+
+#### accumulator( \[x] )
+
+If provided an input value `x`, the accumulator function returns an updated exponentially weighted variance. If not provided an input value `x`, the accumulator function returns the current exponentially weighted variance.
+
+```javascript
+var accumulator = nanewvariance( 0.5 );
+
+var v = accumulator();
+// returns null
+
+v = accumulator( 2.0 );
+// returns 0
+
+v = accumulator( 4.0 );
+// returns 1
+
+v = accumulator( NaN );
+// returns 1
+
+v = accumulator( 5.0 );
+// returns 1.5
+
+v = accumulator();
+// returns 1.5
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   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.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var nanewvariance = require( '@stdlib/stats/incr/nanewvariance' );
+
+var accumulator;
+var v;
+var i;
+
+// Initialize an accumulator with smoothing factor α = 0.5:
+accumulator = nanewvariance( 0.5 );
+
+// For each simulated datum, update the exponentially weighted variance...
+for ( i = 0; i < 100; i++ ) {
+    // With a 20% chance, provide NaN to test that invalid inputs are ignored:
+    v = ( randu() < 0.2 ) ? NaN : randu() * 100.0;
+    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">
+
+</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">
+
+[exponentially weighted variance]: https://en.wikipedia.org/wiki/EWMA_chart
+
+</section>
+
+<!-- /.links -->

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 nanewvariance = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = nanewvariance( 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 = nanewvariance( 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();
+});

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

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+
+{{alias}}( α )
+    Returns an accumulator function which incrementally computes an
+    exponentially weighted variance, where α is a smoothing factor between 0 and
+    1. This accumulator ignores any input values that are `NaN`.
+
+    If provided a value, the accumulator function returns an updated variance.
+    If not provided a value, the accumulator function returns the current
+    variance.
+
+    If provided `NaN` or a value which, when used in computations, results in
+    `NaN`, that input is ignored and the accumulated variance remains unchanged.
+
+    Parameters
+    ----------
+    α: number
+        Smoothing factor (value between 0 and 1).
+
+    Returns
+    -------
+    acc: Function
+        Accumulator function.
+
+    Examples
+    --------
+    > var accumulator = {{alias}}( 0.5 );
+    > var v = accumulator()
+    null
+    > v = accumulator( 2.0 )
+    0
+    > v = accumulator( 4.0 )
+    1
+    > v = accumulator( NaN )
+    1
+    > v = accumulator( 5.0 )
+    1.5
+    > v = accumulator()
+    1.5
+
+    See Also
+    --------
+