time-to-botec

Benchmark sampling in different programming languages
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README.md (3697B)

      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.
     18 
     19 -->
     20 
     21 # Quantile Function
     22 
     23 > [Lévy][levy-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [Lévy][levy-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:levy_quantile_function" align="center" raw="Q(p;\mu,c)= \mu + \frac{c}{2 \cdot \operatorname{erfcinv}(p)^2}" alt="Quantile function for a Lévy distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p;\mu,c)= \mu + \frac{c}{2 \cdot \operatorname{erfcinv}(p)^2}" data-equation="eq:levy_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/levy/quantile/docs/img/equation_levy_quantile_function.svg" alt="Quantile function for a Lévy distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p < 1`, where `µ` is the location parameter and `c > 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/levy/quantile' );
     50 ```
     51 
     52 #### quantile( p, mu, c )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [Lévy][levy-distribution] distribution with parameters `mu` (location parameter) and `c` (scale parameter).
     55 
     56 ```javascript
     57 var y = quantile( 0.5, 0.0, 1.0 );
     58 // returns ~2.198
     59 
     60 y = quantile( 0.2, 4.0, 2.0 );
     61 // returns ~5.218
     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 `c <= 0`, the function returns `NaN`.
     88 
     89 ```javascript
     90 var y = quantile( 0.4, 0.0, -1.0 );
     91 // returns NaN
     92 
     93 y = quantile( 0.4, 0.0, 0.0 );
     94 // returns NaN
     95 ```
     96 
     97 #### quantile.factory( mu, c )
     98 
     99 Returns a function for evaluating the [quantile function][quantile-function] of a [Lévy][levy-distribution] distribution with parameters `mu` and `c`.
    100 
    101 ```javascript
    102 var myQuantile = quantile.factory( 10.0, 2.0 );
    103 
    104 var y = myQuantile( 0.2 );
    105 // returns ~11.218
    106 
    107 y = myQuantile( 0.8 );
    108 // returns ~41.16
    109 ```
    110 
    111 </section>
    112 
    113 <!-- /.usage -->
    114 
    115 <section class="examples">
    116 
    117 ## Examples
    118 
    119 <!-- eslint no-undef: "error" -->
    120 
    121 ```javascript
    122 var randu = require( '@stdlib/random/base/randu' );
    123 var quantile = require( '@stdlib/stats/base/dists/levy/quantile' );
    124 
    125 var mu;
    126 var c;
    127 var p;
    128 var y;
    129 var i;
    130 
    131 for ( i = 0; i < 10; i++ ) {
    132     p = randu();
    133     mu = randu() * 10.0;
    134     c = randu() * 10.0;
    135     y = quantile( p, mu, c );
    136     console.log( 'p: %d, µ: %d, c: %d, Q(p;µ,c): %d', p, mu, c, y );
    137 }
    138 ```
    139 
    140 </section>
    141 
    142 <!-- /.examples -->
    143 
    144 <section class="links">
    145 
    146 [levy-distribution]: https://en.wikipedia.org/wiki/L%C3%A9vy_distribution
    147 
    148 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    149 
    150 </section>
    151 
    152 <!-- /.links -->