README.md (3570B)
1 <!-- 2 3 @license Apache-2.0 4 5 Copyright (c) 2018 The Stdlib Authors. 6 7 Licensed under the Apache License, Version 2.0 (the "License"); 8 you may not use this file except in compliance with the License. 9 You may obtain a copy of the License at 10 11 http://www.apache.org/licenses/LICENSE-2.0 12 13 Unless required by applicable law or agreed to in writing, software 14 distributed under the License is distributed on an "AS IS" BASIS, 15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 16 See the License for the specific language governing permissions and 17 limitations under the License. 18 19 --> 20 21 # Skewness 22 23 > [Rayleigh][rayleigh-distribution] distribution [skewness][skewness]. 24 25 <!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. --> 26 27 <section class="intro"> 28 29 The [skewness][skewness] for a [Rayleigh][rayleigh-distribution] random variable is 30 31 <!-- <equation class="equation" label="eq:rayleigh_skewness" align="center" raw="\operatorname{skew}\left( X \right) = \frac{2{\sqrt{\pi }}(\pi -3)}{(4-\pi )^{3/2}}" alt="Skewness for a Rayleigh distribution."> --> 32 33 <div class="equation" align="center" data-raw-text="\operatorname{skew}\left( X \right) = \frac{2{\sqrt{\pi }}(\pi -3)}{(4-\pi )^{3/2}}" data-equation="eq:rayleigh_skewness"> 34 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/rayleigh/skewness/docs/img/equation_rayleigh_skewness.svg" alt="Skewness for a Rayleigh distribution."> 35 <br> 36 </div> 37 38 <!-- </equation> --> 39 40 where `σ > 0` is the scale parameter. 41 42 </section> 43 44 <!-- /.intro --> 45 46 <!-- Package usage documentation. --> 47 48 <section class="usage"> 49 50 ## Usage 51 52 ```javascript 53 var skewness = require( '@stdlib/stats/base/dists/rayleigh/skewness' ); 54 ``` 55 56 #### skewness( sigma ) 57 58 Returns the [skewness][skewness] of a [Rayleigh][rayleigh-distribution] distribution with scale parameter `sigma`. 59 60 ```javascript 61 var y = skewness( 9.0 ); 62 // returns ~0.631 63 64 y = skewness( 3.5 ); 65 // returns ~0.631 66 ``` 67 68 If provided `sigma < 0`, the function returns `NaN`. 69 70 ```javascript 71 var y = skewness( -1.0 ); 72 // returns NaN 73 ``` 74 75 </section> 76 77 <!-- /.usage --> 78 79 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 80 81 <section class="notes"> 82 83 </section> 84 85 <!-- /.notes --> 86 87 <!-- Package usage examples. --> 88 89 <section class="examples"> 90 91 ## Examples 92 93 <!-- eslint no-undef: "error" --> 94 95 ```javascript 96 var randu = require( '@stdlib/random/base/randu' ); 97 var round = require( '@stdlib/math/base/special/round' ); 98 var skewness = require( '@stdlib/stats/base/dists/rayleigh/skewness' ); 99 100 var sigma; 101 var y; 102 var i; 103 104 for ( i = 0; i < 10; i++ ) { 105 sigma = randu() * 20.0; 106 y = skewness( sigma ); 107 console.log( 'σ: %d, skew(X,σ): %d', sigma.toFixed( 4 ), y.toFixed( 4 ) ); 108 } 109 ``` 110 111 </section> 112 113 <!-- /.examples --> 114 115 <!-- 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. --> 116 117 <section class="references"> 118 119 </section> 120 121 <!-- /.references --> 122 123 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 124 125 <section class="links"> 126 127 [rayleigh-distribution]: https://en.wikipedia.org/wiki/Rayleigh_distribution 128 129 [skewness]: https://en.wikipedia.org/wiki/Skewness 130 131 </section> 132 133 <!-- /.links -->