README.md (6923B)
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 # Beta 22 23 > Beta distribution. 24 25 <section class="usage"> 26 27 ## Usage 28 29 ```javascript 30 var beta = require( '@stdlib/stats/base/dists/beta' ); 31 ``` 32 33 #### beta 34 35 [Beta][beta-distribution] distribution. 36 37 ```javascript 38 var dist = beta; 39 // returns {...} 40 ``` 41 42 The namespace contains the following distribution functions: 43 44 <!-- <toc pattern="*+(cdf|pdf|mgf|quantile)*"> --> 45 46 <div class="namespace-toc"> 47 48 - <span class="signature">[`cdf( x, alpha, beta )`][@stdlib/stats/base/dists/beta/cdf]</span><span class="delimiter">: </span><span class="description">beta distribution cumulative distribution function.</span> 49 - <span class="signature">[`logcdf( x, alpha, beta )`][@stdlib/stats/base/dists/beta/logcdf]</span><span class="delimiter">: </span><span class="description">beta distribution logarithm of cumulative distribution function.</span> 50 - <span class="signature">[`logpdf( x, alpha, beta )`][@stdlib/stats/base/dists/beta/logpdf]</span><span class="delimiter">: </span><span class="description">beta distribution logarithm of probability density function (PDF).</span> 51 - <span class="signature">[`mgf( t, alpha, beta )`][@stdlib/stats/base/dists/beta/mgf]</span><span class="delimiter">: </span><span class="description">beta distribution moment-generating function (MGF).</span> 52 - <span class="signature">[`pdf( x, alpha, beta )`][@stdlib/stats/base/dists/beta/pdf]</span><span class="delimiter">: </span><span class="description">beta distribution probability density function (PDF).</span> 53 - <span class="signature">[`quantile( p, alpha, beta )`][@stdlib/stats/base/dists/beta/quantile]</span><span class="delimiter">: </span><span class="description">beta distribution quantile function.</span> 54 55 </div> 56 57 <!-- </toc> --> 58 59 The namespace contains the following functions for calculating distribution properties: 60 61 <!-- <toc pattern="*+(entropy|kurtosis|mean|median|mode|skewness|stdev|variance)*"> --> 62 63 <div class="namespace-toc"> 64 65 - <span class="signature">[`entropy( alpha, beta )`][@stdlib/stats/base/dists/beta/entropy]</span><span class="delimiter">: </span><span class="description">beta distribution differential entropy.</span> 66 - <span class="signature">[`kurtosis( alpha, beta )`][@stdlib/stats/base/dists/beta/kurtosis]</span><span class="delimiter">: </span><span class="description">beta distribution excess kurtosis.</span> 67 - <span class="signature">[`mean( alpha, beta )`][@stdlib/stats/base/dists/beta/mean]</span><span class="delimiter">: </span><span class="description">beta distribution expected value.</span> 68 - <span class="signature">[`median( alpha, beta )`][@stdlib/stats/base/dists/beta/median]</span><span class="delimiter">: </span><span class="description">beta distribution median.</span> 69 - <span class="signature">[`mode( alpha, beta )`][@stdlib/stats/base/dists/beta/mode]</span><span class="delimiter">: </span><span class="description">beta distribution mode.</span> 70 - <span class="signature">[`skewness( alpha, beta )`][@stdlib/stats/base/dists/beta/skewness]</span><span class="delimiter">: </span><span class="description">beta distribution skewness.</span> 71 - <span class="signature">[`stdev( alpha, beta )`][@stdlib/stats/base/dists/beta/stdev]</span><span class="delimiter">: </span><span class="description">beta distribution standard deviation.</span> 72 - <span class="signature">[`variance( alpha, beta )`][@stdlib/stats/base/dists/beta/variance]</span><span class="delimiter">: </span><span class="description">beta distribution variance.</span> 73 74 </div> 75 76 <!-- </toc> --> 77 78 The namespace contains a constructor function for creating a [beta][beta-distribution] distribution object. 79 80 <!-- <toc pattern="*ctor*"> --> 81 82 <div class="namespace-toc"> 83 84 - <span class="signature">[`Beta( [alpha, beta] )`][@stdlib/stats/base/dists/beta/ctor]</span><span class="delimiter">: </span><span class="description">beta distribution constructor.</span> 85 86 </div> 87 88 <!-- </toc> --> 89 90 ```javascript 91 var Beta = require( '@stdlib/stats/base/dists/beta' ).Beta; 92 var dist = new Beta( 2.0, 4.0 ); 93 94 var mu = dist.mean; 95 // returns ~0.333 96 ``` 97 98 </section> 99 100 <!-- /.usage --> 101 102 <section class="examples"> 103 104 ## Examples 105 106 <!-- TODO: better examples --> 107 108 <!-- eslint no-undef: "error" --> 109 110 ```javascript 111 var objectKeys = require( '@stdlib/utils/keys' ); 112 var beta = require( '@stdlib/stats/base/dists/beta' ); 113 114 console.log( objectKeys( beta ) ); 115 ``` 116 117 </section> 118 119 <!-- /.examples --> 120 121 <section class="links"> 122 123 [beta-distribution]: https://en.wikipedia.org/wiki/Beta_distribution 124 125 <!-- <toc-links> --> 126 127 [@stdlib/stats/base/dists/beta/ctor]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/ctor 128 129 [@stdlib/stats/base/dists/beta/entropy]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/entropy 130 131 [@stdlib/stats/base/dists/beta/kurtosis]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/kurtosis 132 133 [@stdlib/stats/base/dists/beta/mean]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/mean 134 135 [@stdlib/stats/base/dists/beta/median]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/median 136 137 [@stdlib/stats/base/dists/beta/mode]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/mode 138 139 [@stdlib/stats/base/dists/beta/skewness]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/skewness 140 141 [@stdlib/stats/base/dists/beta/stdev]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/stdev 142 143 [@stdlib/stats/base/dists/beta/variance]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/variance 144 145 [@stdlib/stats/base/dists/beta/cdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/cdf 146 147 [@stdlib/stats/base/dists/beta/logcdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/logcdf 148 149 [@stdlib/stats/base/dists/beta/logpdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/logpdf 150 151 [@stdlib/stats/base/dists/beta/mgf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/mgf 152 153 [@stdlib/stats/base/dists/beta/pdf]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/pdf 154 155 [@stdlib/stats/base/dists/beta/quantile]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dists/beta/quantile 156 157 <!-- </toc-links> --> 158 159 </section> 160 161 <!-- /.links -->