time-to-botec

Benchmark sampling in different programming languages
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README.md (3821B)

      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
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     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 # Probability Density Function
     22 
     23 > [Rayleigh][rayleigh-distribution] distribution probability density function (PDF).
     24 
     25 <section class="intro">
     26 
     27 The [probability density function][pdf] (PDF) for a [Rayleigh][rayleigh-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:rayleigh_pdf" align="center" raw="f(x;\sigma) = \begin{cases} \frac{x}{\sigma^2} e^{-x^2/(2\sigma^2)} &amp; \text{ for } x \ge 0 \\ 0 & \text{ otherwise } \end{cases}" alt="Probability density function (PDF) for a Rayleigh distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="f(x;\sigma) = \begin{cases} \frac{x}{\sigma^2} e^{-x^2/(2\sigma^2)} &amp;amp; \text{ for } x \ge 0 \\ 0 &amp; \text{ otherwise } \end{cases}" data-equation="eq:rayleigh_pdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/rayleigh/pdf/docs/img/equation_rayleigh_pdf.svg" alt="Probability density function (PDF) for a Rayleigh distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 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 pdf = require( '@stdlib/stats/base/dists/rayleigh/pdf' );
     50 ```
     51 
     52 #### pdf( x, sigma )
     53 
     54 Evaluates the [probability density function][pdf] for a [Rayleigh][rayleigh-distribution] distribution with scale parameter `sigma`.
     55 
     56 ```javascript
     57 var y = pdf( 0.3, 1.0 );
     58 // returns ~0.287
     59 
     60 y = pdf( 2.0, 0.8 );
     61 // returns ~0.137
     62 
     63 y = pdf( -1.0, 0.5 );
     64 // returns 0.0
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = pdf( NaN, 1.0 );
     71 // returns NaN
     72 
     73 y = pdf( 0.0, NaN );
     74 // returns NaN
     75 ```
     76 
     77 If provided `sigma < 0`, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = pdf( 2.0, -1.0 );
     81 // returns NaN
     82 ```
     83 
     84 If provided `sigma = 0`, the function evaluates the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `0`.
     85 
     86 ```javascript
     87 var y = pdf( -2.0, 0.0 );
     88 // returns 0.0
     89 
     90 y = pdf( 0.0, 0.0 );
     91 // returns Infinity
     92 
     93 y = pdf( 2.0, 0.0 );
     94 // returns 0.0
     95 ```
     96 
     97 #### pdf.factory( sigma )
     98 
     99 Returns a function for evaluating the [probability density function][pdf] (PDF) of a [Rayleigh][rayleigh-distribution] distribution with parameter `sigma` (scale parameter).
    100 
    101 ```javascript
    102 var myPDF = pdf.factory( 4.0 );
    103 
    104 var y = myPDF( 6.0 );
    105 // returns ~0.122
    106 
    107 y = myPDF( 4.0 );
    108 // returns ~0.152
    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 pdf = require( '@stdlib/stats/base/dists/rayleigh/pdf' );
    124 
    125 var sigma;
    126 var x;
    127 var y;
    128 var i;
    129 
    130 for ( i = 0; i < 10; i++ ) {
    131     x = randu() * 10.0;
    132     sigma = randu() * 10.0;
    133     y = pdf( x, sigma );
    134     console.log( 'x: %d, σ: %d, f(x;σ): %d', x.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
    135 }
    136 ```
    137 
    138 </section>
    139 
    140 <!-- /.examples -->
    141 
    142 <section class="links">
    143 
    144 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    145 
    146 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function
    147 
    148 [rayleigh-distribution]: https://en.wikipedia.org/wiki/Rayleigh_distribution
    149 
    150 </section>
    151 
    152 <!-- /.links -->