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feat: add stats/base/dists/bradford/skewness
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‎lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Skewness
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> [Bradford][bradford-distribution] distribution [skewness][skewness].
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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The [skewness][skewness] for a [Bradford][bradford-distribution] random variable with shape parameter.`c` is
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<!-- <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."> -->
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```math
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\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)}
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```
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<!-- </equation> -->
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where `c` is the shape parameter.
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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<section class="usage">
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## Usage
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```javascript
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var skewness = require( '@stdlib/stats/base/dists/bradford/skewness' );
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```
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#### skewness( c )
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Returns the [skewness][skewness] of a [Bradford][bradford-distribution] distribution with degrees of freedom `c`.
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```javascript
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var v = skewness( 9.0 );
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// returns ~0.772
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v = skewness( 0.5 );
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// returns ~0.140
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```
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If provided `c <= 0`, the function returns `NaN`.
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```javascript
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var v = skewness( -1.0 );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- Package usage examples. -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var skewness = require( '@stdlib/stats/base/dists/bradford/skewness' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var c = uniform( 10, 0.1, 10.0 );
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var v;
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var i;
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for ( i = 0; i < 10; i++ ) {
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v = skewness( c[ i ] );
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console.log( 'c: %d, Skew(X;c): %d', c[ i ].toFixed( 4 ), v.toFixed( 4 ) );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- 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. -->
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<section class="references">
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</section>
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<!-- /.references -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[bradford-distribution]: https://en.wikipedia.org/wiki/Bradford%27s_law
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[skewness]: https://en.wikipedia.org/wiki/Skewness
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var EPS = require( '@stdlib/constants/float64/eps' );
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var pkg = require( './../package.json' ).name;
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var skewness = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var len;
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var c;
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var y;
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var i;
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len = 100;
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c = uniform( 100, EPS, 20.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = skewness( c[ i % len ] );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

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

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{{alias}}( c )
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Returns the skewness of a Bradford distribution.
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If provided `NaN` as any argument, the function returns `NaN`.
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If provided `c <= 0`, the function returns `NaN`.
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Parameters
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----------
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c: number
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Shape Parameter.
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Returns
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-------
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out: number
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Skewness.
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Examples
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--------
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> var v = {{alias}}( 11.0 )
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~0.829
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> v = {{alias}}( 1.5 )
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~0.316
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See Also
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--------
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‎lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/docs/types/index.d.ts‎

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2019 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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// TypeScript Version: 4.1
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/**
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* Returns the skewness of a Bradford distribution.
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*
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* ## Notes
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*
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* - If provided `c <= 0`, the function returns `NaN`.
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*
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* @param c - shape parameter
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* @returns skewness
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*
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* @example
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* var v = skewness( 9.0 );
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* // returns ~0.772
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*
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* @example
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* var v = skewness( 1.0 );
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* // returns ~0.239
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*
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* @example
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* var v = skewness( -0.2 );
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* // returns NaN
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*
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* @example
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* var v = skewness( NaN );
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* // returns NaN
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*/
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declare function skewness( c: number ): number;
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// EXPORTS //
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export = skewness;

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

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2019 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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import skewness = require( './index' );
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// TESTS //
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// The function returns a number...
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{
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skewness( 9.0 ); // $ExpectType number
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}
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// The compiler throws an error if the function is provided a value other than a number...
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{
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skewness( true ); // $ExpectError
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skewness( false ); // $ExpectError
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skewness( null ); // $ExpectError
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skewness( undefined ); // $ExpectError
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skewness( '5' ); // $ExpectError
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skewness( [] ); // $ExpectError
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skewness( {} ); // $ExpectError
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skewness( ( x: number ): number => x ); // $ExpectError
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}
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// The compiler throws an error if the function is provided insufficient arguments...
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{
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skewness(); // $ExpectError
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}

‎lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/examples/index.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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var uniform = require( '@stdlib/random/array/uniform' );
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var skewness = require( './../lib' );
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var c = uniform( 10, 0.1, 10.0 );
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var v;
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var i;
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for ( i = 0; i < 10; i++ ) {
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v = skewness( c[ i ] );
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console.log( 'c: %d, Skew(X;c): %d', c[ i ].toFixed( 4 ), v.toFixed( 4 ) );
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}

‎lib/node_modules/@stdlib/stats/base/dists/bradford/skewness/lib/index.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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/**
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* Bradford distribution skewness.
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*
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* @module @stdlib/stats/base/dists/bradford/skewness
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*
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* @example
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* var skewness = require( '@stdlib/stats/base/dists/bradford/skewness' );
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*
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* var v = skewness( 11.0 );
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* // returns ~0.829
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*
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* v = skewness( 1.5 );
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* // returns ~0.316
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*/
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// MODULES //
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var main = require( './main.js' );
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// EXPORTS //
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module.exports = main;

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