README.md (3061B)
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 # Quantile Function 22 23 > [Degenerate distribution][degenerate-distribution] [quantile function][quantile-function]. 24 25 <section class="intro"> 26 27 The [quantile function][quantile-function] for a [degenerate][degenerate-distribution] random variable is 28 29 <!-- <equation class="equation" label="eq:degenerate_quantile_function" align="center" raw="Q(p;\mu) = \inf \left\{x \in {\mathbb {R}}:p \leq F(x;\mu)\right\} = \mu" alt="Quantile function for a degenerate distribution."> --> 30 31 <div class="equation" align="center" data-raw-text="Q(p;\mu) = \inf \left\{x \in {\mathbb {R}}:p \leq F(x;\mu)\right\} = \mu" data-equation="eq:degenerate_quantile_function"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@e1fbdee688c5409e4cc6b0cd06d90b1cd2abd67c/lib/node_modules/@stdlib/stats/base/dists/degenerate/quantile/docs/img/equation_degenerate_quantile_function.svg" alt="Quantile function for a degenerate distribution."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 for `0 <= p <= 1` and where `µ` is the constant value of the distribution. 39 40 </section> 41 42 <!-- /.intro --> 43 44 <section class="usage"> 45 46 ## Usage 47 48 ```javascript 49 var quantile = require( '@stdlib/stats/base/dists/degenerate/quantile' ); 50 ``` 51 52 #### quantile( p, mu ) 53 54 Evaluates the [quantile function][quantile-function] of a [degenerate distribution][degenerate-distribution] centered at `mu`. 55 56 ```javascript 57 var y = quantile( 0.3, 8.0 ); 58 // returns 8.0 59 60 y = quantile( 0.9, 8.0 ); 61 // returns 8.0 62 ``` 63 64 #### quantile.factory( mu ) 65 66 Returns a function for evaluating the [quantile function][quantile-function] of a [degenerate distribution][degenerate-distribution] centered at `mu`. 67 68 ```javascript 69 var myquantile = quantile.factory( 10.0 ); 70 71 var y = myquantile( 0.2 ); 72 // returns 10.0 73 74 y = myquantile( 1.1 ); 75 // returns NaN 76 ``` 77 78 </section> 79 80 <!-- /.usage --> 81 82 <section class="examples"> 83 84 ## Examples 85 86 <!-- eslint no-undef: "error" --> 87 88 ```javascript 89 var randu = require( '@stdlib/random/base/randu' ); 90 var quantile = require( '@stdlib/stats/base/dists/degenerate/quantile' ); 91 92 var mu; 93 var p; 94 var y; 95 var i; 96 97 for ( i = 0; i < 10; i++ ) { 98 p = randu(); 99 mu = ( randu()*10.0 ) - 5.0; 100 y = quantile( p, mu ); 101 console.log( 'p: %d, µ: %d, Q(p;µ): %d', p, mu, y ); 102 } 103 ``` 104 105 </section> 106 107 <!-- /.examples --> 108 109 <section class="links"> 110 111 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function 112 113 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution 114 115 </section> 116 117 <!-- /.links -->