time-to-botec

Benchmark sampling in different programming languages
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README.md (4014B)

      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
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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.
     18 
     19 -->
     20 
     21 # Quantile Function
     22 
     23 > [Cauchy][cauchy-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [Cauchy][cauchy-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:cauchy_cauchy_quantile_function" align="center" raw="Q(p; x_0,\gamma) = x_0 + \gamma\,\tan\left[\pi\left(p-\tfrac{1}{2}\right)\right]" alt="Quantile function for a Cauchy distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p; x_0,\gamma) = x_0 + \gamma\,\tan\left[\pi\left(p-\tfrac{1}{2}\right)\right]" data-equation="eq:cauchy_cauchy_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/cauchy/quantile/docs/img/equation_cauchy_cauchy_quantile_function.svg" alt="Quantile function for a Cauchy distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p <= 1`, where `x0` is the location parameter and `gamma > 0` is the scale parameter.
     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/cauchy/quantile' );
     50 ```
     51 
     52 #### quantile( p, x0, gamma )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [Cauchy][cauchy-distribution] distribution with parameters `x0` (location parameter) and `gamma > 0` (scale parameter).
     55 
     56 ```javascript
     57 var y = quantile( 0.5, 0.0, 1.0 );
     58 // returns 0.0
     59 
     60 y = quantile( 0.2, 4.0, 2.0 );
     61 // returns ~1.247
     62 
     63 y = quantile( 0.9, 4.0, 2.0 );
     64 // returns ~10.155
     65 ```
     66 
     67 If provided a probability `p` outside the interval `[0,1]`, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = quantile( 1.9, 0.0, 1.0 );
     71 // returns NaN
     72 
     73 y = quantile( -0.1, 0.0, 1.0 );
     74 // returns NaN
     75 ```
     76 
     77 If provided `NaN` as any argument, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = quantile( NaN, 0.0, 1.0 );
     81 // returns NaN
     82 
     83 y = quantile( 0.0, NaN, 1.0 );
     84 // returns NaN
     85 
     86 y = quantile( 0.0, 0.0, NaN );
     87 // returns NaN
     88 ```
     89 
     90 If provided `gamma <= 0`, the function returns `NaN`.
     91 
     92 ```javascript
     93 var y = quantile( 0.4, 0.0, -1.0 );
     94 // returns NaN
     95 
     96 y = quantile( 0.4, 0.0, 0.0 );
     97 // returns NaN
     98 ```
     99 
    100 #### quantile.factory( x0, gamma )
    101 
    102 Returns a function for evaluating the [quantile function][quantile-function] of a [Cauchy][cauchy-distribution] distribution with location parameter `x0` and scale parameter `gamma > 0`.
    103 
    104 ```javascript
    105 var myquantile = quantile.factory( 10.0, 2.0 );
    106 
    107 var y = myquantile( 0.2 );
    108 // returns ~7.247
    109 
    110 y = myquantile( 0.8 );
    111 // returns ~12.753
    112 ```
    113 
    114 </section>
    115 
    116 <!-- /.usage -->
    117 
    118 <section class="examples">
    119 
    120 ## Examples
    121 
    122 <!-- eslint no-undef: "error" -->
    123 
    124 ```javascript
    125 var randu = require( '@stdlib/random/base/randu' );
    126 var EPS = require( '@stdlib/constants/float64/eps' );
    127 var quantile = require( '@stdlib/stats/base/dists/cauchy/quantile' );
    128 
    129 var gamma;
    130 var x0;
    131 var p;
    132 var y;
    133 var i;
    134 
    135 for ( i = 0; i < 10; i++ ) {
    136     p = randu();
    137     x0 = ( randu()*10.0 ) - 5.0;
    138     gamma = ( randu()*20.0 ) + EPS;
    139     y = quantile( p, gamma, x0 );
    140     console.log( 'p: %d, x0: %d, γ: %d, Q(p;x0,γ): %d', p.toFixed(4), x0.toFixed(4), gamma.toFixed(4), y.toFixed(4) );
    141 }
    142 ```
    143 
    144 </section>
    145 
    146 <!-- /.examples -->
    147 
    148 <section class="links">
    149 
    150 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    151 
    152 [cauchy-distribution]: https://en.wikipedia.org/wiki/Cauchy_distribution
    153 
    154 </section>
    155 
    156 <!-- /.links -->