time-to-botec

Benchmark sampling in different programming languages
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README.md (3573B)

      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
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     19 -->
     20 
     21 # Mean
     22 
     23 > [Rayleigh][rayleigh-distribution] distribution [expected value][expected-value].
     24 
     25 <!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
     26 
     27 <section class="intro">
     28 
     29 The [expected value][expected-value] for a [Rayleigh][rayleigh-distribution] random variable is
     30 
     31 <!-- <equation class="equation" label="eq:rayleigh_expectation" align="center" raw="\mathbb{E}\left[ X \right] = \sigma \sqrt{\dfrac{\pi}{2}}" alt="Expected value for a Rayleigh distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="\mathbb{E}\left[ X \right] = \sigma \sqrt{\dfrac{\pi}{2}}" data-equation="eq:rayleigh_expectation">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/rayleigh/mean/docs/img/equation_rayleigh_expectation.svg" alt="Expected value for a Rayleigh distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `σ > 0` is the scale parameter.
     41 
     42 </section>
     43 
     44 <!-- /.intro -->
     45 
     46 <!-- Package usage documentation. -->
     47 
     48 <section class="usage">
     49 
     50 ## Usage
     51 
     52 ```javascript
     53 var mean = require( '@stdlib/stats/base/dists/rayleigh/mean' );
     54 ```
     55 
     56 #### mean( sigma )
     57 
     58 Returns the [expected value][expected-value] of a [Rayleigh][rayleigh-distribution] distribution with scale parameter `sigma`.
     59 
     60 ```javascript
     61 var y = mean( 9.0 );
     62 // returns ~11.28
     63 
     64 y = mean( 1.5 );
     65 // returns ~1.88
     66 ```
     67 
     68 If provided `sigma < 0`, the function returns `NaN`.
     69 
     70 ```javascript
     71 var y = mean( -1.0 );
     72 // returns NaN
     73 
     74 y = mean( -0.1 );
     75 // returns NaN
     76 ```
     77 
     78 </section>
     79 
     80 <!-- /.usage -->
     81 
     82 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
     83 
     84 <section class="notes">
     85 
     86 </section>
     87 
     88 <!-- /.notes -->
     89 
     90 <!-- Package usage examples. -->
     91 
     92 <section class="examples">
     93 
     94 ## Examples
     95 
     96 <!-- eslint no-undef: "error" -->
     97 
     98 ```javascript
     99 var randu = require( '@stdlib/random/base/randu' );
    100 var round = require( '@stdlib/math/base/special/round' );
    101 var mean = require( '@stdlib/stats/base/dists/rayleigh/mean' );
    102 
    103 var sigma;
    104 var y;
    105 var i;
    106 
    107 for ( i = 0; i < 10; i++ ) {
    108     sigma = randu() * 20.0;
    109     y = mean( sigma );
    110     console.log( 'σ: %d, E(X,σ): %d', sigma.toFixed( 4 ), y.toFixed( 4 ) );
    111 }
    112 ```
    113 
    114 </section>
    115 
    116 <!-- /.examples -->
    117 
    118 <!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    119 
    120 <section class="references">
    121 
    122 </section>
    123 
    124 <!-- /.references -->
    125 
    126 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    127 
    128 <section class="links">
    129 
    130 [rayleigh-distribution]: https://en.wikipedia.org/wiki/Rayleigh_distribution
    131 
    132 [expected-value]: https://en.wikipedia.org/wiki/Expected_value
    133 
    134 </section>
    135 
    136 <!-- /.links -->