README.md (3633B)
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 # Cumulative Distribution Function 22 23 > [Arcsine][arcsine-distribution] distribution [cumulative distribution function][cdf]. 24 25 <section class="intro"> 26 27 The [cumulative distribution function][cdf] for an [arcsine][arcsine-distribution] random variable is 28 29 <!-- <equation class="equation" label="eq:arcsine_cdf" align="center" raw="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" alt="Cumulative distribution function for an arcsine distribution."> --> 30 31 <div class="equation" align="center" data-raw-text="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" data-equation="eq:arcsine_cdf"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/cdf/docs/img/equation_arcsine_cdf.svg" alt="Cumulative distribution function for an arcsine distribution."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 where `a` is the minimum support and `b` is the maximum support. The parameters must satisfy `a < b`. 39 40 </section> 41 42 <!-- /.intro --> 43 44 <section class="usage"> 45 46 ## Usage 47 48 ```javascript 49 var cdf = require( '@stdlib/stats/base/dists/arcsine/cdf' ); 50 ``` 51 52 #### cdf( x, a, b ) 53 54 Evaluates the [cumulative distribution function][cdf] (CDF) for an [arcsine][arcsine-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support). 55 56 ```javascript 57 var y = cdf( 9.0, 0.0, 10.0 ); 58 // returns ~0.795 59 60 y = cdf( 0.5, 0.0, 2.0 ); 61 // returns ~0.333 62 63 y = cdf( -Infinity, 2.0, 4.0 ); 64 // returns 0.0 65 66 y = cdf( +Infinity, 2.0, 4.0 ); 67 // returns 1.0 68 ``` 69 70 If provided `NaN` as any argument, the function returns `NaN`. 71 72 ```javascript 73 var y = cdf( NaN, 0.0, 1.0 ); 74 // returns NaN 75 76 y = cdf( 0.0, NaN, 1.0 ); 77 // returns NaN 78 79 y = cdf( 0.0, 0.0, NaN ); 80 // returns NaN 81 ``` 82 83 If provided `a >= b`, the function returns `NaN`. 84 85 ```javascript 86 var y = cdf( 1.0, 2.5, 2.0 ); 87 // returns NaN 88 ``` 89 90 #### cdf.factory( a, b ) 91 92 Returns a function for evaluating the [cumulative distribution function][cdf] of an [arcsine][arcsine-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support). 93 94 ```javascript 95 var mycdf = cdf.factory( 0.0, 10.0 ); 96 var y = mycdf( 0.5 ); 97 // returns ~0.144 98 99 y = mycdf( 8.0 ); 100 // returns ~0.705 101 ``` 102 103 </section> 104 105 <!-- /.usage --> 106 107 <section class="examples"> 108 109 ## Examples 110 111 <!-- eslint no-undef: "error" --> 112 113 ```javascript 114 var randu = require( '@stdlib/random/base/randu' ); 115 var cdf = require( '@stdlib/stats/base/dists/arcsine/cdf' ); 116 117 var a; 118 var b; 119 var x; 120 var y; 121 var i; 122 123 for ( i = 0; i < 25; i++ ) { 124 x = ( randu()*20.0 ) - 10.0; 125 a = ( randu()*20.0 ) - 20.0; 126 b = a + ( randu()*40.0 ); 127 y = cdf( x, a, b ); 128 console.log( 'x: %d, a: %d, b: %d, F(x;a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) ); 129 } 130 ``` 131 132 </section> 133 134 <!-- /.examples --> 135 136 <section class="links"> 137 138 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function 139 140 [arcsine-distribution]: https://en.wikipedia.org/wiki/Arcsine_distribution 141 142 </section> 143 144 <!-- /.links -->