feat: add stats/base/dists/bradford/skewness

lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/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.
+
+-->
+
+# Skewness
+
+> [Bradford][bradford-distribution] distribution [skewness][skewness].
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+The [skewness][skewness] for a [Bradford][bradford-distribution] random variable with shape parameter.`c` is
+
+<!-- <equation class="equation" label="eq:bradford_skewness" align="center" raw="\operatorname{skew}\left( c \right) = \frac{\sqrt{2}\,\Bigl(12c^2 - 9c\,\log(1+c)(c+2) +2\,(\log(1+c))^2\,(c(c+3)+3)\Bigr)}{\sqrt{c\,\Bigl(c\,(\log(1+c)-2)+2\log(1+c)\Bigr)}\Bigl(3c\,(\log(1+c)-2)+6\log(1+c)\Bigr)}" alt="Skewness for a bradford distribution."> -->
+
+```math
+\mathop{\mathrm{skew}}\left( c \right) = \frac{\sqrt{2}\,\Bigl(12c^2 - 9c\,\log(1+c)(c+2) + 2\,(\log(1+c))^2\,(c(c+3)+3)\Bigr)}{\sqrt{c\,\Bigl(c\,(\log(1+c)-2)+2\log(1+c)\Bigr)}\Bigl(3c\,(\log(1+c)-2)+6\log(1+c)\Bigr)}
+```
+
+<!-- </equation> -->
+
+where `c` is the shape parameter.
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var skewness = require( '@stdlib/stats/base/dists/bradford/skewness' );
+```
+
+#### skewness( c )
+
+Returns the [skewness][skewness] of a [Bradford][bradford-distribution] distribution with degrees of freedom `c`.
+
+```javascript
+var v = skewness( 9.0 );
+// returns ~0.772
+
+v = skewness( 0.5 );
+// returns ~0.140
+```
+
+If provided `c <= 0`, the function returns `NaN`.
+
+```javascript
+var v = skewness( -1.0 );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- Package usage examples. -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var skewness = require( '@stdlib/stats/base/dists/bradford/skewness' );
+var uniform = require( '@stdlib/random/array/uniform' );
+
+var c = uniform( 10, 0.1, 10.0 );
+
+var v;
+var i;
+for ( i = 0; i < 10; i++ ) {
+    v = skewness( c[ i ] );
+    console.log( 'c: %d, Skew(X;c): %d', c[ i ].toFixed( 4 ), v.toFixed( 4 ) );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="references">
+
+</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">
+
+[bradford-distribution]: https://en.wikipedia.org/wiki/Bradford%27s_law
+
+[skewness]: https://en.wikipedia.org/wiki/Skewness
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var pkg = require( './../package.json' ).name;
+var skewness = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var len;
+	var c;
+	var y;
+	var i;
+
+	len = 100;
+	c = uniform( 100, EPS, 20.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = skewness( c[ i % len ] );
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/docs/repl.txt

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+
+{{alias}}( c )
+    Returns the skewness of a Bradford distribution.
+
+    If provided `NaN` as any argument, the function returns `NaN`.
+
+    If provided `c <= 0`, the function returns `NaN`.
+
+    Parameters
+    ----------
+    c: number
+        Shape Parameter.
+
+    Returns
+    -------
+    out: number
+        Skewness.
+
+    Examples
+    --------
+    > var v = {{alias}}( 11.0 )
+    ~0.829
+    > v = {{alias}}( 1.5 )
+    ~0.316
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/docs/types/index.d.ts

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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.
+*/
+
+// TypeScript Version: 4.1
+
+/**
+* Returns the skewness of a Bradford distribution.
+*
+* ## Notes
+*
+* -   If provided `c <= 0`, the function returns `NaN`.
+*
+* @param c - shape parameter
+* @returns skewness
+*
+* @example
+* var v = skewness( 9.0 );
+* // returns ~0.772
+*
+* @example
+* var v = skewness( 1.0 );
+* // returns ~0.239
+*
+* @example
+* var v = skewness( -0.2 );
+* // returns NaN
+*
+* @example
+* var v = skewness( NaN );
+* // returns NaN
+*/
+declare function skewness( c: number ): number;
+
+
+// EXPORTS //
+
+export = skewness;

lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/docs/types/test.ts

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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.
+*/
+
+import skewness = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+	skewness( 9.0 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a value other than a number...
+{
+	skewness( true ); // $ExpectError
+	skewness( false ); // $ExpectError
+	skewness( null ); // $ExpectError
+	skewness( undefined ); // $ExpectError
+	skewness( '5' ); // $ExpectError
+	skewness( [] ); // $ExpectError
+	skewness( {} ); // $ExpectError
+	skewness( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided insufficient arguments...
+{
+	skewness(); // $ExpectError
+}

lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/examples/index.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';
+
+var uniform = require( '@stdlib/random/array/uniform' );
+var skewness = require( './../lib' );
+
+var c = uniform( 10, 0.1, 10.0 );
+
+var v;
+var i;
+for ( i = 0; i < 10; i++ ) {
+	v = skewness( c[ i ] );
+	console.log( 'c: %d, Skew(X;c): %d', c[ i ].toFixed( 4 ), v.toFixed( 4 ) );
+}

lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/lib/index.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';
+
+/**
+* Bradford distribution skewness.
+*
+* @module @stdlib/stats/base/dists/bradford/skewness
+*
+* @example
+* var skewness = require( '@stdlib/stats/base/dists/bradford/skewness' );
+*
+* var v = skewness( 11.0 );
+* // returns ~0.829
+*
+* v = skewness( 1.5 );
+* // returns ~0.316
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;