diff --git a/lib/node_modules/@stdlib/stats/incr/mskewness/README.md b/lib/node_modules/@stdlib/stats/incr/mskewness/README.md
new file mode 100644
index 000000000000..e841819d082e
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/README.md
@@ -0,0 +1,214 @@
+
+
+# incrmskewness
+
+> Compute moving [corrected sample skewness][sample-skewness] incrementally.
+
+
+
+The [skewness][sample-skewness] for a random variable `X` is defined as
+
+
+
+```math
+\mathop{\mathrm{Skewness}}[X] = \mathrm{E}\biggl[ \biggl( \frac{X - \mu}{\sigma} \biggr)^3 \biggr]
+```
+
+
+
+
+
+For a sample of `n` values, the [sample skewness][sample-skewness] is
+
+
+
+```math
+b_1 = \frac{m_3}{s^3} = \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}
+```
+
+
+
+
+
+where `m_3` is the sample third central moment and `s` is the sample standard deviation.
+
+An alternative definition for the [sample skewness][sample-skewness] which includes an adjustment factor (and is the implemented definition) is
+
+
+
+```math
+G_1 = \frac{n^2}{(n-1)(n-2)} \frac{m_3}{s^3} = \frac{\sqrt{n(n-1)}}{n-2} \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}
+```
+
+
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var incrmskewness = require( '@stdlib/stats/incr/mskewness' );
+```
+
+#### incrmskewness( W )
+
+Returns an accumulator `function` which incrementally computes a moving [corrected sample skewness][sample-skewness] over a sliding window of size `W`.
+
+```javascript
+var accumulator = incrmskewness( 5 );
+```
+
+#### accumulator( \[x] )
+
+If provided an input value `x`, the accumulator function returns an updated moving [corrected sample skewness][sample-skewness]. If not provided an input value `x`, the accumulator function returns the current moving [corrected sample skewness][sample-skewness].
+
+```javascript
+var accumulator = incrmskewness( 5 );
+
+var skewness = accumulator();
+// returns null
+
+skewness = accumulator( 2.0 );
+// returns null
+
+skewness = accumulator( -5.0 );
+// returns null
+
+skewness = accumulator( -10.0 );
+// returns ~0.492
+
+skewness = accumulator();
+// returns ~0.492
+```
+
+
+
+
+
+
+
+## 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 **at least** `W-1` 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 randu = require( '@stdlib/random/base/randu' );
+var incrmskewness = require( '@stdlib/stats/incr/mskewness' );
+
+var accumulator;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrmskewness( 3 );
+
+// For each simulated datum, update the corrected sample skewness...
+for ( i = 0; i < 100; i++ ) {
+ v = randu() * 100.0;
+ accumulator( v );
+}
+console.log( accumulator() );
+```
+
+
+
+
+
+* * *
+
+
+
+## References
+
+- Joanes, D. N., and C. A. Gill. 1998. "Comparing measures of sample skewness and kurtosis." _Journal of the Royal Statistical Society: Series D (The Statistician)_ 47 (1). Blackwell Publishers Ltd: 183–89. doi:[10.1111/1467-9884.00122][@joanes:1998].
+
+
+
+
+
+
+
+
+
+* * *
+
+## See Also
+
+- [`@stdlib/stats/incr/kurtosis`][@stdlib/stats/incr/kurtosis]: compute a corrected sample excess kurtosis incrementally.
+- [`@stdlib/stats/incr/mean`][@stdlib/stats/incr/mean]: compute an arithmetic mean incrementally.
+- [`@stdlib/stats/incr/stdev`][@stdlib/stats/incr/stdev]: compute a corrected sample standard deviation incrementally.
+- [`@stdlib/stats/incr/summary`][@stdlib/stats/incr/summary]: compute a statistical summary incrementally.
+- [`@stdlib/stats/incr/variance`][@stdlib/stats/incr/variance]: compute an unbiased sample variance incrementally.
+
+
+
+
+
+
+
+
+
+[sample-skewness]: https://en.wikipedia.org/wiki/Skewness
+
+[@joanes:1998]: http://onlinelibrary.wiley.com/doi/10.1111/1467-9884.00122/
+
+
+
+[@stdlib/stats/incr/kurtosis]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/kurtosis
+
+[@stdlib/stats/incr/mean]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mean
+
+[@stdlib/stats/incr/stdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/stdev
+
+[@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/mskewness/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/incr/mskewness/benchmark/benchmark.js
new file mode 100644
index 000000000000..7a7e5edbae57
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/benchmark/benchmark.js
@@ -0,0 +1,78 @@
+/**
+* @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 incrmskewness = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var f;
+ var i;
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ f = incrmskewness( ( i % 5 ) + 1 );
+ 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 v;
+ var i;
+ var x;
+
+ len = 100;
+ x = new Float64Array( len );
+ for ( i = 0; i < len; i++ ) {
+ x[ i ] = uniform( 0.0, 1.0 );
+ }
+
+ acc = incrmskewness( 5 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ v = acc( x[ i % len ] );
+ 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/mskewness/docs/img/equation_adjusted_sample_skewness.svg b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/img/equation_adjusted_sample_skewness.svg
new file mode 100644
index 000000000000..3277353af222
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/img/equation_adjusted_sample_skewness.svg
@@ -0,0 +1,171 @@
+
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/mskewness/docs/img/equation_sample_skewness.svg b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/img/equation_sample_skewness.svg
new file mode 100644
index 000000000000..147334d80f8b
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/img/equation_sample_skewness.svg
@@ -0,0 +1,131 @@
+
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/mskewness/docs/img/equation_skewness.svg b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/img/equation_skewness.svg
new file mode 100644
index 000000000000..45650ae35b70
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/img/equation_skewness.svg
@@ -0,0 +1,59 @@
+
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/mskewness/docs/repl.txt b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/repl.txt
new file mode 100644
index 000000000000..f63ae2903803
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/repl.txt
@@ -0,0 +1,43 @@
+{{alias}}( W )
+ Returns an accumulator function which incrementally computes a moving
+ corrected sample skewness.
+
+ The `W` parameter defines the window size (i.e., the number of values
+ over which to compute the skewness).
+
+ If provided a value, the accumulator function returns an updated corrected
+ sample skewness. If not provided a value, the accumulator function returns
+ the current corrected sample skewness.
+
+ As `W` values are needed to fill the window buffer, the first `W-1`
+ returned values are calculated from smaller sample sizes
+ (provided at least `3` values have been accumulated).
+ Until the window is full, each returned value is calculated
+ from all provided values.
+
+ Parameters
+ ----------
+ W: integer
+ Window size.
+
+ Returns
+ -------
+ acc: Function
+ Accumulator function.
+
+ Examples
+ --------
+ > var accumulator = {{alias}}( 3 );
+ > var v = accumulator( 2.0 )
+ null
+ > v = accumulator( -5.0 )
+ null
+ > v = accumulator( -10.0 )
+ ~0.492
+ > v = accumulator( 5.0 )
+ ~0.935
+ > v = accumulator()
+ ~0.935
+
+ See Also
+ --------
diff --git a/lib/node_modules/@stdlib/stats/incr/mskewness/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/types/index.d.ts
new file mode 100644
index 000000000000..1110de9609e2
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/types/index.d.ts
@@ -0,0 +1,72 @@
+/*
+* @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 a value, the accumulator function returns an updated corrected sample skewness. If not provided a value, the accumulator function returns the current corrected sample skewness.
+*
+* ## 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
+* @returns corrected sample skewness or null
+*/
+type accumulator = ( x?: number ) => number | null;
+
+/**
+* Returns an accumulator function which incrementally computes a moving corrected sample skewness.
+*
+* ## Notes
+*
+* - If provided a value, the accumulator function returns an updated corrected sample skewness. If not provided a value, the accumulator function returns the current corrected sample skewness.
+* - If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for at least `W` invocations.
+*
+* @param W - window size
+* @returns accumulator function
+*
+* @example
+* var accumulator = incrmskewness( 3 );
+*
+* var skewness = accumulator();
+* // returns null
+*
+* skewness = accumulator( 2.0 );
+* // returns null
+*
+* skewness = accumulator( -5.0 );
+* // returns null
+*
+* skewness = accumulator( -10.0 );
+* // returns ~0.492
+*
+* skewness = accumulator( 5.0 );
+* // returns ~0.935
+*
+* skewness = accumulator();
+* // returns ~0.935
+*/
+declare function incrmskewness( W: number ): accumulator;
+
+
+// EXPORTS //
+
+export = incrmskewness;
diff --git a/lib/node_modules/@stdlib/stats/incr/mskewness/docs/types/test.ts b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/types/test.ts
new file mode 100644
index 000000000000..c7be01d7640f
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/docs/types/test.ts
@@ -0,0 +1,67 @@
+/*
+* @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 incrmskewness = require( './index' );
+
+
+// TESTS //
+
+// The function returns an accumulator function...
+{
+ incrmskewness( 3 ); // $ExpectType accumulator
+}
+
+// The compiler throws an error if the function is provided invalid arguments...
+{
+ incrmskewness( '5' ); // $ExpectError
+ incrmskewness( true ); // $ExpectError
+ incrmskewness( false ); // $ExpectError
+ incrmskewness( null ); // $ExpectError
+ incrmskewness( [] ); // $ExpectError
+ incrmskewness( {} ); // $ExpectError
+ incrmskewness( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an invalid number of arguments...
+{
+ incrmskewness(); // $ExpectError
+ incrmskewness( 3, 2 ); // $ExpectError
+}
+
+// The function returns an accumulator function which returns an accumulated result...
+{
+ const acc = incrmskewness( 3 );
+
+ acc(); // $ExpectType number | null
+ acc( 2 ); // $ExpectType number | null
+ acc( -5 ); // $ExpectType number | null
+ acc( 10 ); // $ExpectType number | null
+}
+
+// The compiler throws an error if the returned accumulator function is provided invalid arguments...
+{
+ const acc = incrmskewness( 5 );
+
+ acc( '5' ); // $ExpectError
+ acc( true ); // $ExpectError
+ acc( false ); // $ExpectError
+ acc( null ); // $ExpectError
+ acc( [] ); // $ExpectError
+ acc( {} ); // $ExpectError
+ acc( ( x: number ): number => x ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/mskewness/examples/index.js b/lib/node_modules/@stdlib/stats/incr/mskewness/examples/index.js
new file mode 100644
index 000000000000..e67a4a0d50c1
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/examples/index.js
@@ -0,0 +1,44 @@
+/**
+* @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 randu = require( '@stdlib/random/base/randu' );
+var incrmskewness = require( './../lib' );
+
+var accumulator;
+var mskewness;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrmskewness( 5 );
+
+// For each simulated datum, update the moving corrected sample skewness...
+console.log( '\nValue\tSkewness\n' );
+
+for ( i = 0; i < 100; i++ ) {
+ v = randu() * 100.0;
+ mskewness = accumulator( v );
+ if ( i < 2 ) {
+ console.log( '%s\t%s', v.toFixed( 4 ), mskewness );
+ } else {
+ console.log( '%s\t%s', v.toFixed( 4 ), mskewness.toFixed( 4 ) );
+ }
+}
+console.log( '\nFinal moving skewness: %d\n', accumulator() );
diff --git a/lib/node_modules/@stdlib/stats/incr/mskewness/lib/index.js b/lib/node_modules/@stdlib/stats/incr/mskewness/lib/index.js
new file mode 100644
index 000000000000..e142c69c7787
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/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 moving corrected sample skewness incrementally.
+*
+* @module @stdlib/stats/incr/mskewness
+*
+* @example
+* var incrmskewness = require( '@stdlib/stats/incr/mskewness' );
+*
+* var accumulator = incrmskewness( 3 );
+*
+* var mskewness = accumulator();
+* // returns null
+*
+* mskewness = accumulator( 2.0 );
+* // returns null
+*
+* mskewness = accumulator( -5.0 );
+* // returns null
+*
+* mskewness = accumulator( -10.0 );
+* // returns ~0.492
+*
+* mskewness = accumulator( 5.0 );
+* // returns ~0.935
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/stats/incr/mskewness/lib/main.js b/lib/node_modules/@stdlib/stats/incr/mskewness/lib/main.js
new file mode 100644
index 000000000000..cabf345d3894
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/lib/main.js
@@ -0,0 +1,226 @@
+/**
+* @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 isPositiveInteger = require( '@stdlib/assert/is-positive-integer' ).isPrimitive;
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var Float64Array = require( '@stdlib/array/float64' );
+var format = require( '@stdlib/string/format' );
+
+
+// MAIN //
+
+/**
+* Returns an accumulator function which incrementally computes a moving corrected sample skewness.
+*
+* ## Method
+*
+* The algorithm computes the corrected sample skewness using the formula for `G_1` in [Joanes and Gill 1998][@joanes:1998]. Updates are performed using an extension of Welford's algorithm for sliding windows.
+*
+* ## References
+*
+* - Joanes, D. N., and C. A. Gill. 1998. "Comparing measures of sample skewness and kurtosis." _Journal of the Royal Statistical Society: Series D (The Statistician)_ 47 (1). Blackwell Publishers Ltd: 183–89. doi:[10.1111/1467-9884.00122][@joanes:1998].
+*
+* [@joanes:1998]: http://dx.doi.org/10.1111/1467-9884.00122
+*
+* @param {PositiveInteger} W - window size
+* @throws {TypeError} must provide a positive integer
+* @returns {Function} accumulator function
+*
+* @example
+* var accumulator = incrmskewness( 3 );
+*
+* var skewness = accumulator();
+* // returns null
+*
+* skewness = accumulator( 2.0 );
+* // returns null
+*
+* skewness = accumulator( -5.0 );
+* // returns null
+*
+* skewness = accumulator( -10.0 );
+* // returns ~0.492
+*
+* skewness = accumulator( 5.0 );
+* // returns ~0.935
+*
+* skewness = accumulator();
+* // returns ~0.935
+*/
+function incrmskewness( W ) {
+ var deltaN;
+ var term1;
+ var delta;
+ var mean;
+ var buf;
+ var tmp;
+ var g1;
+ var M2;
+ var M3;
+ var i;
+ var N;
+
+ if ( !isPositiveInteger( W ) ) {
+ throw new TypeError( format( 'invalid argument. Must provide a positive integer. Value: `%s`.', W ) );
+ }
+ buf = new Float64Array( W );
+ mean = 0.0;
+ M2 = 0.0;
+ M3 = 0.0;
+ i = -1;
+ N = 0;
+
+ return accumulator;
+
+ /**
+ * If provided a value, the accumulator function returns an updated corrected sample skewness. If not provided a value, the accumulator function returns the current corrected sample skewness.
+ *
+ * @private
+ * @param {number} [x] - new value
+ * @returns {(number|null)} corrected sample skewness or null
+ */
+ function accumulator( x ) {
+ var meanOld;
+ var M2Old;
+ var v;
+ var k;
+
+ if ( arguments.length === 0 ) {
+ if ( N < 3 ) {
+ return ( isnan( M3 ) ) ? NaN : null;
+ }
+ // Calculate the population skewness:
+ g1 = sqrt( N ) * M3 / pow( M2, 1.5 );
+
+ // Return the corrected sample skewness:
+ return sqrt( N * ( N - 1 ) ) * g1 / ( N - 2 );
+ }
+
+ // Update the index for managing the circular buffer:
+ i = ( i + 1 ) % W;
+
+ // Case: incoming value is NaN, so the accumulated statistics are automatically NaN...
+ if ( isnan( x ) ) {
+ M2 = NaN;
+ M3 = NaN;
+ mean = NaN;
+ N = W; // explicitly set to avoid `N < W` branch
+ }
+ // Case: initial window...
+ else if ( N < W ) {
+ N += 1;
+ delta = x - mean;
+ deltaN = delta / N;
+ term1 = delta * deltaN * ( N - 1 );
+
+ tmp = term1 * deltaN * ( N - 2 );
+ tmp -= 3.0 * deltaN * M2;
+ M3 += tmp;
+
+ M2 += term1;
+ mean += deltaN;
+ }
+ // Case: outgoing value is NaN or current stats are NaN, and, thus, we need to recompute the accumulated values...
+ else if ( isnan( buf[ i ] ) || isnan( M2 ) || isnan( M3 ) ) {
+ N = 0;
+ M2 = 0.0;
+ M3 = 0.0;
+ mean = 0.0;
+
+ // Reconstruct statistics from the buffer (excluding the outgoing value at `i`, adding `x`):
+ for ( k = 0; k < W; k++ ) {
+ v = ( k === i ) ? x : buf[ k ];
+ if ( isnan( v ) ) {
+ N = W;
+ M2 = NaN;
+ M3 = NaN;
+ mean = NaN;
+ break;
+ }
+ N += 1;
+ delta = v - mean;
+ deltaN = delta / N;
+ term1 = delta * deltaN * ( N - 1 );
+
+ tmp = term1 * deltaN * ( N - 2 );
+ tmp -= 3.0 * deltaN * M2;
+ M3 += tmp;
+
+ M2 += term1;
+ mean += deltaN;
+ }
+ }
+ // Case: neither the current stats nor the incoming/outgoing values are NaN, so we update the accumulated values (remove old, add new)...
+ else {
+ // Remove the outgoing value (buf[i]):
+ v = buf[ i ];
+
+ // To remove, we reverse the Welford update. We calculate the mean *before* v was added (which corresponds to N-1). N here is W.
+ meanOld = ( ( N * mean ) - v ) / ( N - 1 );
+
+ delta = v - meanOld;
+ deltaN = delta / N; // This is ( mean - meanOld )
+
+ term1 = delta * deltaN * ( N - 1 );
+
+ // Revert M2 first (order matters relative to add operation, but we need M2_old for M3):
+ M2Old = M2 - term1;
+
+ tmp = term1 * deltaN * ( N - 2 );
+ tmp -= 3.0 * deltaN * M2Old;
+
+ M3 -= tmp;
+ M2 = M2Old;
+ mean = meanOld;
+
+ // Now Add the new value (x)
+ delta = x - mean;
+ deltaN = delta / N;
+ term1 = delta * deltaN * ( N - 1 );
+
+ tmp = term1 * deltaN * ( N - 2 );
+ tmp -= 3.0 * deltaN * M2;
+ M3 += tmp;
+
+ M2 += term1;
+ mean += deltaN;
+ }
+
+ buf[ i ] = x;
+
+ if ( N < 3 ) {
+ return ( isnan( M3 ) ) ? NaN : null;
+ }
+ // Calculate the population skewness:
+ g1 = sqrt( N ) * M3 / pow( M2, 1.5 );
+
+ // Return the corrected sample skewness:
+ return sqrt( N * ( N - 1 ) ) * g1 / ( N - 2 );
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = incrmskewness;
diff --git a/lib/node_modules/@stdlib/stats/incr/mskewness/package.json b/lib/node_modules/@stdlib/stats/incr/mskewness/package.json
new file mode 100644
index 000000000000..0117e9c872c2
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/package.json
@@ -0,0 +1,65 @@
+{
+ "name": "@stdlib/stats/incr/mskewness",
+ "version": "0.0.0",
+ "description": "Compute moving corrected sample skewness 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",
+ "skewness",
+ "sample skewness",
+ "shape",
+ "corrected",
+ "incremental",
+ "accumulator"
+ ]
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/mskewness/test/test.js b/lib/node_modules/@stdlib/stats/incr/mskewness/test/test.js
new file mode 100644
index 000000000000..1d0260ebfc2e
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/mskewness/test/test.js
@@ -0,0 +1,196 @@
+/**
+* @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 abs = require( '@stdlib/math/base/special/abs' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var incrmskewness = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof incrmskewness, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function throws an error if not provided a positive integer', function test( t ) {
+ var values;
+ var i;
+
+ values = [
+ '5',
+ -5.0,
+ 0.0,
+ 3.14,
+ true,
+ false,
+ null,
+ void 0,
+ NaN,
+ [],
+ {},
+ 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() {
+ incrmskewness( value );
+ };
+ }
+});
+
+tape( 'the function returns an accumulator function', function test( t ) {
+ t.strictEqual( typeof incrmskewness( 3 ), 'function', 'returns expected value' );
+ t.end();
+});
+
+tape( 'the accumulator function computes a moving corrected sample skewness incrementally', function test( t ) {
+ var expected;
+ var actual;
+ var delta;
+ var data;
+ var acc;
+ var tol;
+ var i;
+ var N;
+
+ data = [ 3.0, 2.0, 7.0, -1.0, 9.0, -2.0 ];
+ N = data.length;
+
+ expected = [
+ null,
+ null,
+ 1.4578629673213048,
+ 0.4366620845757488,
+ 0.11718750000000001,
+ 0.329176993486849
+ ];
+
+ acc = incrmskewness( 5 );
+
+ for ( i = 0; i < N; i++ ) {
+ actual = acc( data[ i ] );
+ if ( expected[ i ] === null ) {
+ t.strictEqual( actual, expected[i], 'returns expected value for index '+i );
+ } else {
+ delta = abs( actual - expected[ i ] );
+ tol = 1.5 * EPS * abs( expected[ i ] );
+ t.strictEqual( delta <= tol, true, 'within tolerance. Actual: '+actual+'. Expected: '+expected[i]+'. Delta: '+delta+'. Tol: '+tol+'.' );
+ }
+ }
+
+ t.end();
+});
+
+tape( 'if not provided an input value, the accumulator function returns the current skewness', function test( t ) {
+ var expected;
+ var data;
+ var acc;
+ var i;
+
+ data = [ 3.0, 2.0, 7.0, -1.0, 9.0 ];
+ expected = 0.11718750000000001;
+ acc = incrmskewness( 5 );
+ for ( i = 0; i < data.length; i++ ) {
+ acc( data[ i ] );
+ }
+
+ t.strictEqual( acc(), expected, 'returns expected value' );
+ t.end();
+});
+
+tape( 'if data has yet to be provided, the accumulator function returns `null`', function test( t ) {
+ var acc = incrmskewness( 3 );
+ t.strictEqual( acc(), null, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the corrected sample skewness is `null` until at least 3 datums have been provided', function test( t ) {
+ var skewness;
+ var acc;
+
+ acc = incrmskewness( 5 );
+
+ skewness = acc();
+ t.strictEqual( skewness, null, 'returns expected value' );
+
+ skewness = acc( 2.0 );
+ t.strictEqual( skewness, null, 'returns expected value' );
+
+ skewness = acc( 2.0 );
+ t.strictEqual( skewness, null, 'returns expected value' );
+
+ skewness = acc( 3.0 );
+ t.notEqual( skewness, null, 'does not return null' );
+
+ t.end();
+});
+
+tape( 'if provided `NaN`, the accumulated value is `NaN` for at least `W` invocations', function test( t ) {
+ var expected;
+ var actual;
+ var data;
+ var acc;
+ var i;
+
+ acc = incrmskewness( 3 );
+
+ data = [
+ 1.0, // 1
+ 2.0, // 1, 2
+ 3.0, // 1, 2, 3
+ NaN, // 2, 3, NaN
+ 5.0, // 3, NaN, 5
+ 6.0, // NaN, 5, 6
+ 7.0 // 5, 6, 7
+ ];
+
+ expected = [
+ null,
+ null,
+ 0.0,
+ NaN,
+ NaN,
+ NaN,
+ 0.0
+ ];
+
+ for ( i = 0; i < data.length; i++ ) {
+ actual = acc( data[ i ] );
+ if ( expected[ i ] === null ) {
+ t.strictEqual( actual, null, 'returns null for index '+i );
+ } else if ( isnan( expected[ i ] ) ) {
+ t.strictEqual( isnan( actual ), true, 'returns NaN for index '+i );
+ } else {
+ t.strictEqual( actual, expected[ i ], 'returns expected value for window '+i );
+ }
+ }
+ t.end();
+});