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README.md (5140B)

---

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 # Skewness
 
 > [Kumaraswamy's double bounded][kumaraswamy-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 [Kumaraswamy's double bounded][kumaraswamy-distribution] random variable with first shape parameter `a` and second shape parameter `b` is
 
 <!-- <equation class="equation" label="eq:kumaraswamy_skewness" align="center" raw="\operatorname{skew}\left( X \right) = \frac{ m_3 - 3m_1\sigma^2 - m_1^3 }{ \left( \sigma^2 \right)^{3/2} }" alt="Skewness for a Kumaraswamy's double bounded distribution."> -->
 
 <div class="equation" align="center" data-raw-text="\operatorname{skew}\left( X \right) = \frac{ m_3 - 3m_1\sigma^2 - m_1^3 }{ \left( \sigma^2 \right)^{3/2} }" data-equation="eq:kumaraswamy_skewness">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/skewness/docs/img/equation_kumaraswamy_skewness.svg" alt="Skewness for a Kumaraswamy's double bounded distribution.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 where `σ^2` is the [variance][variance] and the raw moments of the distribution are given by
 
 <!-- <equation class="equation" label="eq:kumaraswamy_raw_moments" align="center" raw="m_n = b \, B\left(1+\tfrac{n}{a}, b \right)" alt="Raw moments for a Kumaraswamy's double bounded distribution."> -->
 
 <div class="equation" align="center" data-raw-text="m_n = b \, B\left(1+\tfrac{n}{a}, b \right)" data-equation="eq:kumaraswamy_raw_moments">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/skewness/docs/img/equation_kumaraswamy_raw_moments.svg" alt="Raw moments for a Kumaraswamy's double bounded distribution.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 with `B` denoting the [beta function][beta-function].
 
 </section>
 
 <!-- /.intro -->
 
 <!-- Package usage documentation. -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var skewness = require( '@stdlib/stats/base/dists/kumaraswamy/skewness' );
 ```
 
 #### skewness( a, b )
 
 Returns the [skewness][skewness] of a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution with first shape parameter `a` and second shape parameter `b`.
 
 ```javascript
 var v = skewness( 1.0, 1.0 );
 // returns ~0.0
 
 v = skewness( 4.0, 12.0 );
 // returns ~-0.201
 
 v = skewness( 2.0, 8.0 );
 // returns ~0.384
 ```
 
 If provided `NaN` as any argument, the function returns `NaN`.
 
 ```javascript
 var v = skewness( NaN, 2.0 );
 // returns NaN
 
 v = skewness( 2.0, NaN );
 // returns NaN
 ```
 
 If provided `a <= 0`, the function returns `NaN`.
 
 ```javascript
 var y = skewness( -1.0, 0.5 );
 // returns NaN
 
 y = skewness( 0.0, 0.5 );
 // returns NaN
 ```
 
 If provided `b <= 0`, the function returns `NaN`.
 
 ```javascript
 var y = skewness( 0.5, -1.0 );
 // returns NaN
 
 y = skewness( 0.5, 0.0 );
 // 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 randu = require( '@stdlib/random/base/randu' );
 var skewness = require( '@stdlib/stats/base/dists/kumaraswamy/skewness' );
 
 var a;
 var b;
 var v;
 var i;
 
 for ( i = 0; i < 10; i++ ) {
     a = randu() * 10.0;
     b = randu() * 10.0;
     v = skewness( a, b );
     console.log( 'a: %d, b: %d, skew(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
 }
 ```
 
 </section>
 
 <!-- /.examples -->
 
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 <section class="references">
 
 </section>
 
 <!-- /.references -->
 
 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
 
 <section class="links">
 
 [beta-function]: https://en.wikipedia.org/wiki/Beta_function
 
 [kumaraswamy-distribution]: https://en.wikipedia.org/wiki/Kumaraswamy_distribution
 
 [skewness]: https://en.wikipedia.org/wiki/Skewness
 
 [variance]: https://en.wikipedia.org/wiki/Variance
 
 </section>
 
 <!-- /.links -->