diff --git a/lib/node_modules/@stdlib/stats/incr/wstdev/README.md b/lib/node_modules/@stdlib/stats/incr/wstdev/README.md
new file mode 100644
index 000000000000..a24859fa00ff
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/wstdev/README.md
@@ -0,0 +1,173 @@
+
+
+# incrwstdev
+
+> Compute a [weighted sample standard deviation][weighted-sample-stdev] incrementally.
+
+
+
+The [weighted sample standard deviation][weighted-sample-stdev] is defined as
+
+
+
+```math
+s = \sqrt{\frac{\displaystyle\sum_{i=0}^{n-1} w_{i} \left( x_{i} - \bar{x} \right)^2}{\displaystyle\sum_{i=0}^{n-1} w_{i}}}
+```
+
+
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var incrwstdev = require( '@stdlib/stats/incr/wstdev' );
+```
+
+#### incrwstdev()
+
+Returns an accumulator `function` which incrementally computes a [weighted sample standard deviation][weighted-sample-stdev].
+
+```javascript
+var accumulator = incrwstdev();
+```
+
+#### accumulator( \[x, w] )
+
+If provided an input value `x` and a weight `w`, the accumulator function returns an updated weighted sample standard deviation. If not provided any input values, the accumulator function returns the current weighted sample standard deviation.
+
+```javascript
+var accumulator = incrwstdev();
+
+var s = accumulator( 2.0, 1.0 );
+// returns 0.0
+
+s = accumulator( 3.0, 2.0 );
+// returns ~0.471
+
+s = accumulator( 2.0, 0.1 );
+// returns ~0.478
+
+s = accumulator();
+// returns ~0.478
+```
+
+
+
+
+
+
+
+## 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.
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var uniform = require( '@stdlib/random/base/uniform' );
+var incrwstdev = require( '@stdlib/stats/incr/wstdev' );
+
+var accumulator;
+var v;
+var w;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrwstdev();
+
+// For each simulated datum, update the weighted sample standard deviation...
+for ( i = 0; i < 100; i++ ) {
+ v = uniform( 0.0, 100.0 );
+ w = uniform( 0.0, 100.0 );
+ accumulator( v, w );
+}
+console.log( accumulator() );
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[weighted-sample-stdev]: https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Weighted_sample_variance
+
+
+
+[@stdlib/stats/incr/kurtosis]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/kurtosis
+
+[@stdlib/stats/incr/wmean]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/wmean
+
+[@stdlib/stats/incr/stdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/stdev
+
+[@stdlib/stats/incr/mstdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mstdev
+
+[@stdlib/stats/incr/skewness]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/skewness
+
+[@stdlib/stats/incr/summary]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/summary
+
+[@stdlib/stats/incr/variance]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/variance
+
+
+
+
+
+
diff --git a/lib/node_modules/@stdlib/stats/incr/wstdev/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/incr/wstdev/benchmark/benchmark.js
new file mode 100644
index 000000000000..bfde44f09956
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/wstdev/benchmark/benchmark.js
@@ -0,0 +1,106 @@
+/**
+* @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 Float64Array = require( '@stdlib/array/float64' );
+var uniform = require( '@stdlib/random/base/uniform' );
+var pkg = require( './../package.json' ).name;
+var incrwstdev = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var f;
+ var i;
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ f = incrwstdev();
+ 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 len;
+ var x;
+ var v;
+ var i;
+
+ acc = incrwstdev();
+ len = 100;
+ x = new Float64Array( len );
+ for ( i = 0; i < len; i++ ) {
+ x[ i ] = uniform( 0.0, 1.0 );
+ }
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ v = acc( x[ i % len ], 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();
+});
+
+bench( pkg+'::accumulator,known_mean', function benchmark( b ) {
+ var acc;
+ var len;
+ var x;
+ var v;
+ var i;
+
+ acc = incrwstdev( 3.0 );
+ len = 100;
+ x = new Float64Array( len );
+ for ( i = 0; i < len; i++ ) {
+ x[ i ] = uniform( 0.0, 1.0 );
+ }
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ v = acc( x[ i % len ], 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();
+});
diff --git a/lib/node_modules/@stdlib/stats/incr/wstdev/docs/img/equation_weighted_sample_standard_deviation.svg b/lib/node_modules/@stdlib/stats/incr/wstdev/docs/img/equation_weighted_sample_standard_deviation.svg
new file mode 100644
index 000000000000..b8cd2b76c494
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/wstdev/docs/img/equation_weighted_sample_standard_deviation.svg
@@ -0,0 +1,89 @@
+
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/wstdev/docs/repl.txt b/lib/node_modules/@stdlib/stats/incr/wstdev/docs/repl.txt
new file mode 100644
index 000000000000..d09d84cf54c9
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/wstdev/docs/repl.txt
@@ -0,0 +1,44 @@
+
+{{alias}}( [mean] )
+ Returns an accumulator function which incrementally computes a weighted
+ sample standard deviation.
+
+ If provided arguments, the accumulator function returns an updated weighted
+ sample standard deviation. If not provided arguments, the accumulator
+ function returns the current weighted sample standard deviation.
+
+ 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.
+
+ Parameters
+ ----------
+ mean: number (optional)
+ Known mean.
+
+ Returns
+ -------
+ acc: Function
+ Accumulator function.
+
+ Examples
+ --------
+ > var accumulator = {{alias}}();
+ > var s = accumulator()
+ null
+ > s = accumulator( 2.0, 1.0 )
+ 0.0
+ > s = accumulator( 3.0, 2.0 )
+ ~0.471
+ > s = accumulator( 2.0, 0.1 )
+ ~0.478
+ > s = accumulator()
+ ~0.478
+
+ See Also
+ --------
+
diff --git a/lib/node_modules/@stdlib/stats/incr/wstdev/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/incr/wstdev/docs/types/index.d.ts
new file mode 100644
index 000000000000..7733a565c25d
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/wstdev/docs/types/index.d.ts
@@ -0,0 +1,68 @@
+/*
+* @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.
+*/
+
+// TypeScript Version: 4.1
+
+///
+
+/**
+* If provided both arguments, returns an updated weighted sample standard deviation; otherwise, returns the current weighted sample standard deviation.
+*
+* ## 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 {NonNegativeNumber} [w] - weight
+* @throws {TypeError} second argument must be a nonnegative number
+* @returns weighted sample standard deviation
+*/
+type accumulator = ( x?: number, w?: number ) => number | null;
+
+/**
+* Returns an accumulator function which incrementally computes a weighted sample standard deviation.
+*
+* @returns accumulator function
+*
+* @example
+* var accumulator = incrwstdev();
+*
+* var s = accumulator();
+* // returns null
+*
+* s = accumulator( 2.0, 1.0 );
+* // returns 0.0
+*
+* s = accumulator( 3.0, 2.0 );
+* // returns ~0.471
+*
+* s = accumulator( 2.0, 0.1 );
+* // returns ~0.478
+*
+* s = accumulator();
+* // returns ~0.478
+*
+* @example
+* var accumulator = incrwstdev( 3.0 );
+*/
+declare function incrwstdev(): accumulator;
+
+
+// EXPORTS //
+
+export = incrwstdev;
diff --git a/lib/node_modules/@stdlib/stats/incr/wstdev/docs/types/test.ts b/lib/node_modules/@stdlib/stats/incr/wstdev/docs/types/test.ts
new file mode 100644
index 000000000000..d9980f114fc5
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/wstdev/docs/types/test.ts
@@ -0,0 +1,69 @@
+/*
+* @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.
+*/
+
+import incrwstdev = require( './index' );
+
+
+// TESTS //
+
+// The function returns an accumulator function...
+{
+ incrwstdev(); // $ExpectType accumulator
+}
+
+// The compiler throws an error if the function is provided arguments...
+{
+ incrwstdev( '5' ); // $ExpectError
+ incrwstdev( 5 ); // $ExpectError
+ incrwstdev( true ); // $ExpectError
+ incrwstdev( false ); // $ExpectError
+ incrwstdev( null ); // $ExpectError
+ incrwstdev( undefined ); // $ExpectError
+ incrwstdev( [] ); // $ExpectError
+ incrwstdev( {} ); // $ExpectError
+ incrwstdev( ( x: number ): number => x ); // $ExpectError
+}
+
+// The function returns an accumulator function which returns an accumulated result...
+{
+ const acc = incrwstdev();
+
+ 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 = incrwstdev();
+
+ 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
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/wstdev/examples/index.js b/lib/node_modules/@stdlib/stats/incr/wstdev/examples/index.js
new file mode 100644
index 000000000000..fb7cf6433ef2
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/wstdev/examples/index.js
@@ -0,0 +1,41 @@
+/**
+* @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';
+
+var uniform = require( '@stdlib/random/base/uniform' );
+var incrwstdev = require( './../lib' );
+
+var accumulator;
+var s;
+var x;
+var w;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrwstdev();
+
+// For each simulated datum, update the weighted sample standard deviation...
+console.log( '\nValue\tWeight\tSigma\n' );
+for ( i = 0; i < 100; i++ ) {
+ x = uniform( 0.0, 100.0 );
+ w = uniform( 0.0, 100.0 );
+ s = accumulator( x, w );
+ console.log( '%d\t%d\t%d', x.toFixed( 4 ), w.toFixed( 4 ), s.toFixed( 4 ) );
+}
+console.log( '\nFinal weighted sample standard deviation: %d\n', accumulator() );
diff --git a/lib/node_modules/@stdlib/stats/incr/wstdev/lib/index.js b/lib/node_modules/@stdlib/stats/incr/wstdev/lib/index.js
new file mode 100644
index 000000000000..fcb9fc092d2f
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/wstdev/lib/index.js
@@ -0,0 +1,54 @@
+/**
+* @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';
+
+/**
+* Compute a weighted sample standard deviation incrementally.
+*
+* @module @stdlib/stats/incr/wstdev
+*
+* @example
+* var incrwstdev = require( '@stdlib/stats/incr/wstdev' );
+*
+* var accumulator = incrwstdev();
+*
+* var s = accumulator();
+* // returns null
+*
+* s = accumulator( 2.0, 1.0 );
+* // returns 0.0
+*
+* s = accumulator( 3.0, 2.0 );
+* // returns ~0.471
+*
+* s = accumulator( 2.0, 0.1 );
+* // returns ~0.478
+*
+* s = accumulator();
+* // returns ~0.478
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/stats/incr/wstdev/lib/main.js b/lib/node_modules/@stdlib/stats/incr/wstdev/lib/main.js
new file mode 100644
index 000000000000..b9f442e69caf
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/wstdev/lib/main.js
@@ -0,0 +1,206 @@
+/**
+* @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 isNonNegativeNumber = require( '@stdlib/assert/is-nonnegative-number' ).isPrimitive;
+var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var format = require( '@stdlib/string/format' );
+
+
+// MAIN //
+
+/**
+* Returns an accumulator function which incrementally computes a weighted sample standard deviation.
+*
+* ## Method
+*
+* - The weighted sample standard deviation is defined as
+*
+* ```tex
+* \sigma = \sqrt{\frac{\sum_{i=0}^{n-1} w_i (x_i - \mu)^2}{\sum_{i=0}^{n-1} w_i}}
+* ```
+*
+* where \\( w_i \\) are the weights and \\( \mu \\) is the weighted arithmetic mean.
+*
+* - To derive an incremental formula for computing a weighted sample standard deviation, let:
+*
+* ```tex
+* W_n = \sum_{i=1}^{n} w_i
+* ```
+*
+* - Accordingly:
+*
+* ```tex
+* \begin{align*}
+* \sigma^2 &= \frac{1}{W_n} \sum_{i=1}^{n} w_i (x_i - \mu)^2 \\
+* &= \frac{1}{W_n} \sum_{i=1}^{n} w_i x_i^2 - \mu^2
+* \end{align*}
+* ```
+*
+* - Let:
+*
+* ```tex
+* M2_n = W_n \sigma^2_n = \sum_{i=1}^{n} w_i x_i^2 - W_n \mu_n^2
+* ```
+*
+* - To compute the incremental update for \\(M2_n\\):
+*
+* ```tex
+* \begin{align*}
+* M2_n - M2_{n-1} &= \sum_{i=1}^{n} w_i x_i^2 - W_n \mu_n^2 - \sum_{i=1}^{n-1} w_i x_i^2 + W_{n-1} \mu_{n-1}^2 \\
+* &= w_n x_n^2 - W_n \mu_n^2 + W_{n-1} \mu_{n-1}^2 \\
+* &= w_n x_n^2 - W_n \mu_n^2 + (W_n - w_n) \mu_{n-1}^2 \\
+* &= w_n (x_n^2 - \mu_{n-1}^2) + W_n (\mu_{n-1}^2 - \mu_n^2)
+* \end{align*}
+* ```
+*
+* - Simplify further:
+*
+* ```tex
+* \begin{align*}
+* M2_n - M2_{n-1} &= w_n (x_n - \mu_{n-1}) (x_n - \mu_n) \\
+* M2_n &= M2_{n-1} + w_n (x_n - \mu_{n-1}) (x_n - \mu_n)
+* \end{align*}
+* ```
+*
+* - Finally, compute the weighted sample standard deviation:
+*
+* ```tex
+* \sigma_n = \sqrt{\frac{M2_n}{W_n}}
+* ```
+*
+* - Incrementally updating the weighted sample mean:
+*
+* ```tex
+* \begin{align*}
+* \mu_n &= \mu_{n-1} + \frac{w_n}{W_n} (x_n - \mu_{n-1})
+* \end{align*}
+* ```
+*
+* @param {number} [mean] - mean value
+* @throws {TypeError} must provide a number primitive
+* @returns {Function} accumulator function
+*
+* @example
+* var accumulator = incrwstdev();
+*
+* var s = accumulator();
+* // returns null
+*
+* s = accumulator( 2.0, 1.0 );
+* // returns 0.0
+*
+* s = accumulator( 3.0, 2.0 );
+* // returns ~0.471
+*
+* s = accumulator( 2.0, 0.1 );
+* // returns ~0.478
+*
+* s = accumulator();
+* // returns ~0.478
+*
+* @example
+* var accumulator = incrwstdev( 3.0 );
+*/
+function incrwstdev( mean ) {
+ var delta;
+ var wsum;
+ var FLG;
+ var M2;
+ var mu;
+
+ wsum = 0.0;
+ M2 = 0.0;
+ if ( arguments.length ) {
+ if ( !isNumber( mean ) ) {
+ throw new TypeError( format( 'invalid argument. Must provide a number. Value: `%s`.', mean ) );
+ }
+ mu = mean;
+ return accumulator2;
+ }
+ mu = 0.0;
+ return accumulator1;
+
+ /**
+ * If provided a value, the accumulator function returns an updated weighted sample standard deviation. If not provided a value, the accumulator function returns the current weighted sample standard deviation.
+ *
+ * @private
+ * @param {number} [x] - value
+ * @param {NonNegativeNumber} [w] - weight
+ * @throws {TypeError} second argument must be a nonnegative number
+ * @returns {(number|null)} weighted sample standard deviation or null
+ */
+ function accumulator1( x, w ) {
+ if ( arguments.length === 0 ) {
+ if ( FLG === void 0 ) {
+ return null;
+ }
+ return sqrt( M2 / wsum );
+ }
+ if ( !isNonNegativeNumber( w ) ) {
+ throw new TypeError( format( 'invalid argument. Second argument must be a nonnegative number. Value: `%s`.', w ) );
+ }
+ if ( w === 0.0 ) {
+ return ( FLG === void 0 ) ? null : sqrt( M2 / wsum );
+ }
+ FLG = true;
+ delta = x - mu;
+ wsum += w;
+ mu += ( w / wsum ) * delta;
+ M2 += w * delta * ( x - mu );
+ return sqrt( M2 / wsum );
+ }
+
+ /**
+ * If provided a value, the accumulator function returns an updated weighted sample standard deviation. If not provided a value, the accumulator function returns the current weighted sample standard deviation.
+ *
+ * @private
+ * @param {number} [x] - value
+ * @param {NonNegativeNumber} [w] - weight
+ * @throws {TypeError} second argument must be a nonnegative number
+ * @returns {(number|null)} weighted sample standard deviation or null
+ */
+ function accumulator2( x, w ) {
+ if ( arguments.length === 0 ) {
+ if ( FLG === void 0 ) {
+ return null;
+ }
+ return sqrt( M2 / wsum );
+ }
+ if ( !isNonNegativeNumber( w ) ) {
+ throw new TypeError( format( 'invalid argument. Second argument must be a nonnegative number. Value: `%s`.', w ) );
+ }
+ if ( w === 0.0 ) {
+ return ( FLG === void 0 ) ? null : sqrt( M2 / wsum );
+ }
+ FLG = true;
+ delta = x - mu;
+ wsum += w;
+ M2 += w * delta * delta;
+ return sqrt( M2 / wsum );
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = incrwstdev;
diff --git a/lib/node_modules/@stdlib/stats/incr/wstdev/package.json b/lib/node_modules/@stdlib/stats/incr/wstdev/package.json
new file mode 100644
index 000000000000..10ffc3184538
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/wstdev/package.json
@@ -0,0 +1,67 @@
+{
+ "name": "@stdlib/stats/incr/wstdev",
+ "version": "0.0.0",
+ "description": "Compute a weighted sample standard deviation incrementally.",
+ "license": "Apache-2.0",
+ "author": {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ },
+ "contributors": [
+ {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ }
+ ],
+ "main": "./lib",
+ "directories": {
+ "benchmark": "./benchmark",
+ "doc": "./docs",
+ "example": "./examples",
+ "lib": "./lib",
+ "test": "./test"
+ },
+ "types": "./docs/types",
+ "scripts": {},
+ "homepage": "https://github.com/stdlib-js/stdlib",
+ "repository": {
+ "type": "git",
+ "url": "git://github.com/stdlib-js/stdlib.git"
+ },
+ "bugs": {
+ "url": "https://github.com/stdlib-js/stdlib/issues"
+ },
+ "dependencies": {},
+ "devDependencies": {},
+ "engines": {
+ "node": ">=0.10.0",
+ "npm": ">2.7.0"
+ },
+ "os": [
+ "aix",
+ "darwin",
+ "freebsd",
+ "linux",
+ "macos",
+ "openbsd",
+ "sunos",
+ "win32",
+ "windows"
+ ],
+ "keywords": [
+ "stdlib",
+ "stdmath",
+ "statistics",
+ "stats",
+ "mathematics",
+ "math",
+ "average",
+ "avg",
+ "mean",
+ "arithmetic mean",
+ "central tendency",
+ "incremental",
+ "accumulator",
+ "weighted"
+ ]
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/wstdev/test/test.js b/lib/node_modules/@stdlib/stats/incr/wstdev/test/test.js
new file mode 100644
index 000000000000..7964be5943a5
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/wstdev/test/test.js
@@ -0,0 +1,208 @@
+/**
+* @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 tape = require( 'tape' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var incrwstdev = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof incrwstdev, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function returns an accumulator function', function test( t ) {
+ t.equal( typeof incrwstdev(), 'function', 'returns a function' );
+ t.end();
+});
+
+tape( 'the function returns an accumulator function (known mean)', function test( t ) {
+ t.equal( typeof incrwstdev( 3.0 ), 'function', 'returns a function' );
+ t.end();
+});
+
+tape( 'the function throws an error if provided a non-numeric value', function test( t ) {
+ var values;
+ var i;
+
+ values = [
+ '5',
+ true,
+ false,
+ null,
+ void 0,
+ [],
+ {},
+ function noop() {}
+ ];
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[i] ), TypeError, 'throws an error when provided '+values[i] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ incrwstdev( value );
+ };
+ }
+});
+
+tape( 'the accumulator function ignores zero weights and only updates the weighted sample standard deviation after encountering a non-zero weight', function test( t ) {
+ var acc = incrwstdev();
+ t.equal( acc(), null, 'returns expected value' );
+ t.equal( acc( 2.0, 0.0 ), null, 'returns expected value' );
+ t.equal( acc( 2.0, 2.0 ), 0.0, 'returns expected value' );
+ t.equal( acc( 14.0, 2.0 ), 6.0, 'returns expected value' );
+ t.equal( acc( 25.0, 0.0 ), 6.0, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the accumulator function throws an error if provided a second argument which is not a nonnegative number', function test( t ) {
+ var values;
+ var acc;
+ var i;
+
+ values = [
+ '5',
+ -5.0,
+ NaN,
+ undefined,
+ true,
+ false,
+ null,
+ void 0,
+ [],
+ {},
+ function noop() {}
+ ];
+
+ for ( i = 0; i < values.length; i++ ) {
+ t.throws( badValue( values[i] ), TypeError, 'throws an error when provided '+values[i] );
+ }
+ t.end();
+
+ function badValue( value ) {
+ return function badValue() {
+ acc = incrwstdev();
+ acc( 2.0, value );
+ };
+ }
+});
+
+tape( 'the accumulator function incrementally computes a weighted sample standard deviation', function test( t ) {
+ var wMeanPrev;
+ var expected;
+ var wVarSum;
+ var actual;
+ var delta;
+ var dataX;
+ var dataW;
+ var xwSum;
+ var wMean;
+ var wSum;
+ var acc;
+ var tol;
+ var N;
+ var x;
+ var w;
+ var i;
+
+ dataX = [ 2.0, 3.0, 2.0, 4.0, 3.0, 4.0 ];
+ dataW = [ 1.0, 2.0, 0.1, 1.8, 9.9, 3.6 ];
+ N = dataX.length;
+
+ acc = incrwstdev();
+
+ wMeanPrev = 0.0;
+ wVarSum = 0.0;
+ xwSum = 0.0;
+ wMean = 0.0;
+ wSum = 0.0;
+ for ( i = 0; i < N; i++ ) {
+ x = dataX[ i ];
+ w = dataW[ i ];
+ xwSum += x * w;
+ wSum += w;
+ wMean = xwSum / wSum;
+ wVarSum += w * (x - wMeanPrev) * (x - wMean);
+ wMeanPrev = wMean;
+ expected = sqrt( wVarSum / wSum );
+ actual = acc( x, w );
+ delta = abs( actual - expected );
+ tol = EPS * abs( expected );
+ t.ok( delta <= tol, 'within tolerance. x: ' + x + '. Value: ' + actual + '. Expected: ' + expected + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'if not provided arguments, the accumulator function returns the current weighted sample standard deviation', function test( t ) {
+ var expected;
+ var actual;
+ var delta;
+ var dataX;
+ var dataW;
+ var tol;
+ var acc;
+ var i;
+
+ expected = 2.0;
+ dataX = [ 2.0, 4.0, 6.0, 8.0 ];
+ dataW = [ 1.0, 2.0, 3.0, 4.0 ];
+ acc = incrwstdev();
+ for ( i = 0; i < dataX.length; i++ ) {
+ acc( dataX[ i ], dataW[ i ] );
+ }
+ actual = acc();
+ delta = abs( actual - expected );
+ tol = EPS * abs( expected );
+ t.ok( delta <= tol, 'returns the current accumulated weighted sample standard deviation within tolerance' );
+ t.end();
+});
+
+tape( 'if not provided an input value, the accumulator function returns the current weighted sample standard deviation (known mean)', function test( t ) {
+ var dataX;
+ var dataW;
+ var acc;
+ var i;
+
+ dataX = [ 2.0, 4.0, 6.0, 8.0 ];
+ dataW = [ 1.0, 2.0, 3.0, 4.0 ];
+ acc = incrwstdev( 6.0 );
+ for ( i = 0; i < dataX.length; i++ ) {
+ acc( dataX[ i ], dataW[ i ] );
+ }
+ t.equal( acc(), 2.0, 'returns the current accumulated weighted sample standard deviation' );
+ t.end();
+});
+
+tape( 'if provided `NaN` for a value, the accumulator function returns `NaN`', function test( t ) {
+ var acc = incrwstdev();
+ t.equal( isnan( acc( NaN, 1.0 ) ), true, 'returns NaN' );
+ t.equal( isnan( acc( NaN, 1.0 ) ), true, 'returns NaN' );
+ t.end();
+});