feat: add stats/incr/wvariance incremental weighted variance

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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.
+
+-->
+
+# incrwvariance
+
+> Compute a [weighted variance][weighted-variance] incrementally.
+
+<section class="intro">
+
+The [weighted variance][weighted-variance] is defined as
+
+<!-- <equation class="equation" label="eq:weighted_variance" align="center" raw="\sigma^2_w = \frac{\sum_{i=1}^N w_i (x_i - \mu_w)^2}{\sum_{i=1}^N w_i}" alt="Equation for the weighted variance."> -->
+
+```math
+\sigma^2_w = \frac{\sum_{i=1}^N w_i (x_i - \mu_w)^2}{\sum_{i=1}^N w_i}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\sigma^2_w = \frac{\sum_{i=1}^N w_i (x_i - \mu_w)^2}{\sum_{i=1}^N w_i}" data-equation="eq:weighted_variance">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@adbea9806383f70c982e3191475c874efba1296b/lib/node_modules/@stdlib/stats/incr/wvariance/docs/img/equation_weighted_variance.svg" alt="Equation for the weighted variance.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `μ_w` is the weighted arithmetic mean.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var incrwvariance = require( '@stdlib/stats/incr/wvariance' );
+```
+
+#### incrwvariance()
+
+Returns an accumulator `function` which incrementally computes a [weighted variance][weighted-variance].
+
+```javascript
+var accumulator = incrwvariance();
+```
+
+#### accumulator( \[x, w] )
+
+If provided an input value `x` and a weight `w`, the accumulator function returns an updated weighted variance. If not provided any input values, the accumulator function returns the current variance.
+
+```javascript
+var accumulator = incrwvariance();
+
+var s2 = accumulator( 2.0, 1.0 );
+// returns 0.0
+
+s2 = accumulator( 2.0, 0.5 );
+// returns 0.0
+
+s2 = accumulator( 3.0, 1.5 );
+// returns 0.25
+
+s2 = accumulator();
+// returns 0.25
+```
+
+</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 **all** 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.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var incrwvariance = require( '@stdlib/stats/incr/wvariance' );
+
+var accumulator;
+var v;
+var w;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrwvariance();
+
+// For each simulated datum, update the weighted variance...
+for ( i = 0; i < 100; i++ ) {
+    v = randu() * 100.0;
+    w = randu() * 100.0;
+    accumulator( v, w );
+}
+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">
+
+[weighted-variance]: https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Weighted_sample_variance
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var incrwvariance = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = incrwvariance();
+		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( format( '%s::accumulator', pkg ), function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+
+	acc = incrwvariance();
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu(), 1.0 );
+		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/wvariance/docs/repl.txt

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+
+{{alias}}()
+    Returns an accumulator function which incrementally computes a weighted
+    variance.
+
+    If provided arguments, the accumulator function returns an updated weighted
+    variance. If not provided arguments, the accumulator function returns the
+    current weighted variance.
+
+    If provided `NaN` or a value which, when used in computations, results in
+    `NaN`, the accumulated value is `NaN` for all future invocations.
+
+    The accumulator function accepts two arguments:
+
+    - x: value.
+    - w: weight.
+
+    Returns
+    -------
+    acc: Function
+        Accumulator function.
+
+    Examples
+    --------
+    > var accumulator = {{alias}}();
+    > var s2 = accumulator()
+    null
+    > s2 = accumulator( 2.0, 1.0 )
+    0.0
+    > s2 = accumulator( 2.0, 0.5 )
+    0.0
+    > s2 = accumulator( 3.0, 1.5 )
+    0.25
+    > s2 = accumulator()
+    0.25
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/stats/incr/wvariance/docs/types/index.d.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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.
+*/
+
+// TypeScript Version: 4.1
+
+/// <reference types="@stdlib/types"/>
+
+/**
+* If provided both arguments, returns an updated weighted variance; otherwise, returns the current weighted variance.
+*
+* ## Notes
+*
+* -   If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for all future invocations.
+*
+* @param x - value
+* @param w - weight
+* @returns weighted variance
+*/
+type accumulator = ( x?: number, w?: number ) => number | null;
+
+/**
+* Returns an accumulator function which incrementally computes a weighted variance.
+*
+* @returns accumulator function
+*
+* @example
+* var accumulator = incrwvariance();
+*
+* var s2 = accumulator();
+* // returns null
+*
+* s2 = accumulator( 2.0, 1.0 );
+* // returns 0.0
+*
+* s2 = accumulator( 2.0, 0.5 );
+* // returns 0.0
+*
+* s2 = accumulator( 3.0, 1.5 );
+* // returns 0.25
+*
+* s2 = accumulator();
+* // returns 0.25
+*/
+declare function incrwvariance(): accumulator;
+
+
+// EXPORTS //
+
+export = incrwvariance;

lib/node_modules/@stdlib/stats/incr/wvariance/docs/types/test.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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.
+*/
+
+import incrwvariance = require( './index' );
+
+
+// TESTS //
+
+// The function returns an accumulator function...
+{
+	incrwvariance(); // $ExpectType accumulator
+}
+
+// The compiler throws an error if the function is provided arguments...
+{
+	incrwvariance( '5' ); // $ExpectError
+	incrwvariance( 5 ); // $ExpectError
+	incrwvariance( true ); // $ExpectError
+	incrwvariance( false ); // $ExpectError
+	incrwvariance( null ); // $ExpectError
+	incrwvariance( undefined ); // $ExpectError
+	incrwvariance( [] ); // $ExpectError
+	incrwvariance( {} ); // $ExpectError
+	incrwvariance( ( x: number ): number => x ); // $ExpectError
+}
+
+// The function returns an accumulator function which returns an accumulated result...
+{
+	const acc = incrwvariance();
+
+	acc(); // $ExpectType number | null
+	acc( 3.14, 1.0 ); // $ExpectType number | null
+}
+
+// The compiler throws an error if the returned accumulator function is provided invalid arguments...
+{
+	const acc = incrwvariance();
+
+	acc( '5', 1.0 ); // $ExpectError
+	acc( true, 1.0 ); // $ExpectError
+	acc( false, 1.0 ); // $ExpectError
+	acc( null, 1.0 ); // $ExpectError
+	acc( [], 1.0 ); // $ExpectError
+	acc( {}, 1.0 ); // $ExpectError
+	acc( ( x: number ): number => x, 1.0 ); // $ExpectError
+
+	acc( 3.14, '5' ); // $ExpectError
+	acc( 3.14, true ); // $ExpectError
+	acc( 3.14, false ); // $ExpectError
+	acc( 3.14, null ); // $ExpectError
+	acc( 3.14, [] ); // $ExpectError
+	acc( 3.14, {} ); // $ExpectError
+	acc( 3.14, ( x: number ): number => x ); // $ExpectError
+}