time-to-botec

Benchmark sampling in different programming languages
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README.md (4065B)

      1 <!--
      2 
      3 @license Apache-2.0
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      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 > [Normal][normal-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [normal][normal-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:normal_quantile_function" align="center" raw="Q(p;\mu,\sigma) = \mu+\sigma\sqrt{2}\,\operatorname{erf}^{-1}(2p-1)" alt="Quantile function for a Normal distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p;\mu,\sigma) = \mu+\sigma\sqrt{2}\,\operatorname{erf}^{-1}(2p-1)" data-equation="eq:normal_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/normal/quantile/docs/img/equation_normal_quantile_function.svg" alt="Quantile function for a Normal distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p <= 1`, where `µ` is the mean and `σ` is the standard deviation.
     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/normal/quantile' );
     50 ```
     51 
     52 #### quantile( p, mu, sigma )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [normal][normal-distribution] distribution with parameters `mu` (mean) and `sigma` (standard deviation).
     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 ~2.317
     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 `sigma < 0`, the function returns `NaN`.
     88 
     89 ```javascript
     90 var y = quantile( 0.4, 0.0, -1.0 );
     91 // returns NaN
     92 ```
     93 
     94 If provided `sigma = 0`, the function evaluates the [quantile function][quantile-function] of a [degenerate distribution][degenerate-distribution] centered at `mu`.
     95 
     96 ```javascript
     97 var y = quantile( 0.3, 8.0, 0.0 );
     98 // returns 8.0
     99 
    100 y = quantile( 0.9, 8.0, 0.0 );
    101 // returns 8.0
    102 ```
    103 
    104 #### quantile.factory( mu, sigma )
    105 
    106 Returns a function for evaluating the [quantile function][quantile-function] of a [normal][normal-distribution] distribution with parameters `mu` and `sigma`.
    107 
    108 ```javascript
    109 var myquantile = quantile.factory( 10.0, 2.0 );
    110 
    111 var y = myquantile( 0.2 );
    112 // returns ~8.317
    113 
    114 y = myquantile( 0.8 );
    115 // returns ~11.683
    116 ```
    117 
    118 </section>
    119 
    120 <!-- /.usage -->
    121 
    122 <section class="examples">
    123 
    124 ## Examples
    125 
    126 <!-- eslint no-undef: "error" -->
    127 
    128 ```javascript
    129 var randu = require( '@stdlib/random/base/randu' );
    130 var quantile = require( '@stdlib/stats/base/dists/normal/quantile' );
    131 
    132 var sigma;
    133 var mu;
    134 var p;
    135 var y;
    136 var i;
    137 
    138 for ( i = 0; i < 10; i++ ) {
    139     p = randu();
    140     mu = (randu() * 10.0) - 5.0;
    141     sigma = randu() * 20.0;
    142     y = quantile( p, mu, sigma );
    143     console.log( 'p: %d, µ: %d, σ: %d, Q(p;µ,σ): %d', p, mu, sigma, y );
    144 }
    145 ```
    146 
    147 </section>
    148 
    149 <!-- /.examples -->
    150 
    151 <section class="links">
    152 
    153 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    154 
    155 [normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution
    156 
    157 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    158 
    159 </section>
    160 
    161 <!-- /.links -->