feat: add stats/incr/mskewness

lib/node_modules/@stdlib/stats/incr/mskewness/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.
+
+-->
+
+# incrmskewness
+
+> Compute moving [corrected sample skewness][sample-skewness] incrementally.
+
+<section class="intro">
+
+The [skewness][sample-skewness] for a random variable `X` is defined as
+
+<!-- <equation class="equation" label="eq:skewness" align="center" raw="\operatorname{Skewness}[X] = \mathrm{E}\biggl[ \biggl( \frac{X - \mu}{\sigma} \biggr)^3 \biggr]" alt="Equation for skewness."> -->
+
+```math
+\mathop{\mathrm{Skewness}}[X] = \mathrm{E}\biggl[ \biggl( \frac{X - \mu}{\sigma} \biggr)^3 \biggr]
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\operatorname{Skewness}[X] = \mathrm{E}\biggl[ \biggl( \frac{X - \mu}{\sigma} \biggr)^3 \biggr]" data-equation="eq:skewness">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/mskewness/docs/img/equation_skewness.svg" alt="Equation for skewness.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+For a sample of `n` values, the [sample skewness][sample-skewness] is
+
+<!-- <equation class="equation" label="eq:sample_skewness" align="center" raw="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}}" alt="Equation for the sample skewness."> -->
+
+```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}}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="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}}" data-equation="eq:sample_skewness">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/mskewness/docs/img/equation_sample_skewness.svg" alt="Equation for the sample skewness.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+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
+
+<!-- <equation class="equation" label="eq:adjusted_sample_skewness" align="center" raw="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}}" alt="Equation for the adjusted sample skewness."> -->
+
+```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}}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="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}}" data-equation="eq:adjusted_sample_skewness">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/mskewness/docs/img/equation_adjusted_sample_skewness.svg" alt="Equation for the adjusted sample skewness.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## 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
+```
+
+</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 **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.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```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() );
+```
+
+</section>
+
+<!-- /.examples -->
+
+* * *
+
+<section class="references">
+
+## 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].
+
+</section>
+
+<!-- /.references -->
+
+<!-- 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">
+
+[sample-skewness]: https://en.wikipedia.org/wiki/Skewness
+
+[@joanes:1998]: http://onlinelibrary.wiley.com/doi/10.1111/1467-9884.00122/
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/incr/mskewness/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 Float64Array = require( '@stdlib/array/float64' );
+var uniform = require( '@stdlib/random/base/uniform' );
+var format = require( '@stdlib/string/format' );
+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( format( '%s::accumulator', pkg ), 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();
+});