time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

README.md (3720B)

      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 > [Uniform][uniform-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [continuous uniform][uniform-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:uniform_quantile_function" align="center" raw="Q(p) = a + p (b - a)" alt="Quantile function for a continuous uniform distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p) = a + p (b - a)" data-equation="eq:uniform_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/uniform/quantile/docs/img/equation_uniform_quantile_function.svg" alt="Quantile function for a continuous uniform distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p <= 1`, 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 quantile = require( '@stdlib/stats/base/dists/uniform/quantile' );
     50 ```
     51 
     52 #### quantile( p, a, b )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [continuous uniform][uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
     55 
     56 ```javascript
     57 var y = quantile( 0.8, 0.0, 1.0 );
     58 // returns 0.8
     59 
     60 y = quantile( 0.5, 0.0, 10.0 );
     61 // returns 5.0
     62 ```
     63 
     64 If provided a probability `p` outside the interval `[0,1]`, the function returns `NaN`.
     65 
     66 ```javascript
     67 var y = quantile( 1.9, 0.0, 1.0 );
     68 // returns NaN
     69 
     70 y = quantile( -0.1, 0.0, 1.0 );
     71 // returns NaN
     72 ```
     73 
     74 If provided `NaN` as any argument, the function returns `NaN`.
     75 
     76 ```javascript
     77 var y = quantile( NaN, 0.0, 1.0 );
     78 // returns NaN
     79 
     80 y = quantile( 0.0, NaN, 1.0 );
     81 // returns NaN
     82 
     83 y = quantile( 0.0, 0.0, NaN );
     84 // returns NaN
     85 ```
     86 
     87 If provided `a >= b`, the function returns `NaN`.
     88 
     89 ```javascript
     90 var y = quantile( 0.4, 2.0, 1.0 );
     91 // returns NaN
     92 ```
     93 
     94 #### quantile.factory( a, b )
     95 
     96 Returns a function for evaluating the quantile function of a [continuous uniform][uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
     97 
     98 ```javascript
     99 var myquantile = quantile.factory( 0.0, 4.0 );
    100 y = myquantile( 0.8 );
    101 // returns 3.2
    102 ```
    103 
    104 </section>
    105 
    106 <!-- /.usage -->
    107 
    108 <section class="examples">
    109 
    110 ## Examples
    111 
    112 <!-- eslint no-undef: "error" -->
    113 
    114 ```javascript
    115 var randu = require( '@stdlib/random/base/randu' );
    116 var quantile = require( '@stdlib/stats/base/dists/uniform/quantile' );
    117 
    118 var a;
    119 var b;
    120 var p;
    121 var y;
    122 var i;
    123 
    124 for ( i = 0; i < 25; i++ ) {
    125     p = randu();
    126     a = (randu() * 20.0) - 20.0;
    127     b = a + (randu() * 40.0);
    128     y = quantile( p, a, b );
    129     console.log( 'p: %d, a: %d, b: %d, Q(p;a,b): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
    130 }
    131 ```
    132 
    133 </section>
    134 
    135 <!-- /.examples -->
    136 
    137 <section class="links">
    138 
    139 [uniform-distribution]: https://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29
    140 
    141 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    142 
    143 </section>
    144 
    145 <!-- /.links -->