time-to-botec

Benchmark sampling in different programming languages
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README.md (3743B)

      1 <!--
      2 
      3 @license Apache-2.0
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      5 Copyright (c) 2018 The Stdlib Authors.
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      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
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     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.
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     19 -->
     20 
     21 # Quantile Function
     22 
     23 > [Arcsine][arcsine-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for an [arcsine][arcsine-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:arcsine_quantile_function" align="center" raw="Q(p) = a + ( b - a ) \sin^2 \left( \tfrac{\pi}{2} p \right)" alt="Quantile function for an arcsine distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p) = a + ( b - a ) \sin^2 \left( \tfrac{\pi}{2} p \right)" data-equation="eq:arcsine_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/arcsine/quantile/docs/img/equation_arcsine_quantile_function.svg" alt="Quantile function for an arcsine 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/arcsine/quantile' );
     50 ```
     51 
     52 #### quantile( p, a, b )
     53 
     54 Evaluates the [quantile function][quantile-function] for an [arcsine][arcsine-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 ~0.905
     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 an [arcsine][arcsine-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
     97 
     98 ```javascript
     99 var myquantile = quantile.factory( 0.0, 4.0 );
    100 
    101 var y = myquantile( 0.8 );
    102 // returns ~3.618
    103 ```
    104 
    105 </section>
    106 
    107 <!-- /.usage -->
    108 
    109 <section class="examples">
    110 
    111 ## Examples
    112 
    113 <!-- eslint no-undef: "error" -->
    114 
    115 ```javascript
    116 var randu = require( '@stdlib/random/base/randu' );
    117 var quantile = require( '@stdlib/stats/base/dists/arcsine/quantile' );
    118 
    119 var a;
    120 var b;
    121 var p;
    122 var y;
    123 var i;
    124 
    125 for ( i = 0; i < 25; i++ ) {
    126     p = randu();
    127     a = ( randu()*20.0 ) - 20.0;
    128     b = a + ( randu()*40.0 );
    129     y = quantile( p, a, b );
    130     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 ) );
    131 }
    132 ```
    133 
    134 </section>
    135 
    136 <!-- /.examples -->
    137 
    138 <section class="links">
    139 
    140 [arcsine-distribution]: https://en.wikipedia.org/wiki/Arcsine_distribution
    141 
    142 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    143 
    144 </section>
    145 
    146 <!-- /.links -->