time-to-botec

Benchmark sampling in different programming languages
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README.md (3877B)

      1 <!--
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      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 > [Rayleigh][rayleigh-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [Rayleigh][rayleigh-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:rayleigh_quantile_function" align="center" raw="Q(p;\sigma)=\sigma \sqrt{-\ln[(1 - p)^2]}" alt="Quantile function for a Rayleigh distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p;\sigma)=\sigma \sqrt{-\ln[(1 - p)^2]}" data-equation="eq:rayleigh_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/rayleigh/quantile/docs/img/equation_rayleigh_quantile_function.svg" alt="Quantile function for a Rayleigh distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p < 1`, where `sigma > 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/rayleigh/quantile' );
     50 ```
     51 
     52 #### quantile( p, sigma )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [Rayleigh][rayleigh-distribution] distribution with parameter `sigma` (scale parameter).
     55 
     56 ```javascript
     57 var y = quantile( 0.8, 1.0 );
     58 // returns ~1.794
     59 
     60 y = quantile( 0.5, 4.0 );
     61 // returns ~4.71
     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 );
     68 // returns NaN
     69 
     70 y = quantile( -0.1, 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 );
     78 // returns NaN
     79 
     80 y = quantile( 0.0, NaN);
     81 // returns NaN
     82 ```
     83 
     84 If provided `sigma < 0`, the function returns `NaN`.
     85 
     86 ```javascript
     87 var y = quantile( 0.4, -1.0 );
     88 // returns NaN
     89 ```
     90 
     91 If provided `sigma = 0`, the function evaluates the [quantile function][quantile-function] of a [degenerate distribution][degenerate-distribution] centered at `0`.
     92 
     93 ```javascript
     94 var y = quantile( 0.3, 0.0 );
     95 // returns 0.0
     96 
     97 y = quantile( 0.9, 0.0 );
     98 // returns 0.0
     99 ```
    100 
    101 #### quantile.factory( sigma )
    102 
    103 Returns a function for evaluating the [quantile function][quantile-function] of a [Rayleigh][rayleigh-distribution] distribution with scale parameter `sigma`.
    104 
    105 ```javascript
    106 var myQuantile = quantile.factory( 0.4 );
    107 
    108 y = myQuantile( 0.4 );
    109 // returns ~0.404
    110 
    111 y = myQuantile( 1.0 );
    112 // returns Infinity
    113 ```
    114 
    115 </section>
    116 
    117 <!-- /.usage -->
    118 
    119 <section class="examples">
    120 
    121 ## Examples
    122 
    123 <!-- eslint no-undef: "error" -->
    124 
    125 ```javascript
    126 var randu = require( '@stdlib/random/base/randu' );
    127 var quantile = require( '@stdlib/stats/base/dists/rayleigh/quantile' );
    128 
    129 var sigma;
    130 var p;
    131 var y;
    132 var i;
    133 
    134 for ( i = 0; i < 10; i++ ) {
    135     p = randu();
    136     sigma = randu() * 10.0;
    137     y = quantile( p, sigma );
    138     console.log( 'p: %d, σ: %d, Q(p;σ): %d', p.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
    139 }
    140 ```
    141 
    142 </section>
    143 
    144 <!-- /.examples -->
    145 
    146 <section class="links">
    147 
    148 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    149 
    150 [rayleigh-distribution]: https://en.wikipedia.org/wiki/Rayleigh_distribution
    151 
    152 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    153 
    154 </section>
    155 
    156 <!-- /.links -->