time-to-botec

Benchmark sampling in different programming languages
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README.md (4290B)

      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 > [Beta][beta-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [beta][beta-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:beta_quantile_function" align="center" raw="Q(p;\alpha,\beta)\,=\,\inf\left\{ x\in [0,1] : p \le F(x;\alpha,\beta) \right\}" alt="Quantile function for a beta distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p;\alpha,\beta)\,=\,\inf\left\{ x\in [0,1] : p \le F(x;\alpha,\beta) \right\}" data-equation="eq:beta_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/beta/quantile/docs/img/equation_beta_quantile_function.svg" alt="Quantile function for a beta distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p <= 1`, where `alpha > 0` is the first shape parameter and `beta > 0` is the second shape parameter and `F(x;alpha,beta)` denotes the cumulative distribution function of a [beta][beta-distribution] random variable with parameters `alpha` and `beta`.
     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/beta/quantile' );
     50 ```
     51 
     52 #### quantile( p, alpha, beta )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [beta][beta-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).
     55 
     56 ```javascript
     57 var y = quantile( 0.8, 2.0, 1.0 );
     58 // returns ~0.894
     59 
     60 y = quantile( 0.5, 4.0, 2.0 );
     61 // returns ~0.686
     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, 1.0, 1.0 );
     68 // returns NaN
     69 
     70 y = quantile( -0.1, 1.0, 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, 1.0, 1.0 );
     78 // returns NaN
     79 
     80 y = quantile( 0.5, NaN, 1.0 );
     81 // returns NaN
     82 
     83 y = quantile( 0.5, 1.0, NaN );
     84 // returns NaN
     85 ```
     86 
     87 If provided `alpha <= 0`, the function returns `NaN`.
     88 
     89 ```javascript
     90 var y = quantile( 0.4, -1.0, 1.0 );
     91 // returns NaN
     92 
     93 y = quantile( 0.4, 0.0, 1.0 );
     94 // returns NaN
     95 ```
     96 
     97 If provided `beta <= 0`, the function returns `NaN`.
     98 
     99 ```javascript
    100 var y = quantile( 0.4, 1.0, -1.0 );
    101 // returns NaN
    102 
    103 y = quantile( 0.4, 1.0, 0.0 );
    104 // returns NaN
    105 ```
    106 
    107 #### quantile.factory( alpha, beta )
    108 
    109 Returns a function for evaluating the [quantile function][quantile-function] of a [beta][beta-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).
    110 
    111 ```javascript
    112 var myquantile = quantile.factory( 2.0, 2.0 );
    113 
    114 var y = myquantile( 0.8 );
    115 // returns ~0.713
    116 
    117 y = myquantile( 0.4 );
    118 // returns ~0.433
    119 ```
    120 
    121 </section>
    122 
    123 <!-- /.usage -->
    124 
    125 <section class="examples">
    126 
    127 ## Examples
    128 
    129 <!-- eslint no-undef: "error" -->
    130 
    131 ```javascript
    132 var randu = require( '@stdlib/random/base/randu' );
    133 var EPS = require( '@stdlib/constants/float64/eps' );
    134 var quantile = require( '@stdlib/stats/base/dists/beta/quantile' );
    135 
    136 var alpha;
    137 var beta;
    138 var p;
    139 var y;
    140 var i;
    141 
    142 for ( i = 0; i < 10; i++ ) {
    143     p = randu();
    144     alpha = ( randu()*5.0 ) + EPS;
    145     beta = ( randu()*5.0 ) + EPS;
    146     y = quantile( p, alpha, beta );
    147     console.log( 'p: %d, α: %d, β: %d, Q(p;α,β): %d', p.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
    148 }
    149 ```
    150 
    151 </section>
    152 
    153 <!-- /.examples -->
    154 
    155 <section class="links">
    156 
    157 [beta-distribution]: https://en.wikipedia.org/wiki/Beta_distribution
    158 
    159 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    160 
    161 </section>
    162 
    163 <!-- /.links -->