time-to-botec

Benchmark sampling in different programming languages
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README.md (4217B)

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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");
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     11    http://www.apache.org/licenses/LICENSE-2.0
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     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 > [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution [expected value][mean].
     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 [mean][mean] for a [Kumaraswamy's double bounded][kumaraswamy-distribution] random variable is
     30 
     31 <!-- <equation class="equation" label="eq:kumaraswamy_mean" align="center" raw="\mathbb{E} \left[ X \right] = {b\Gamma(1+{\tfrac {1}{a}})\Gamma(b)}{\Gamma(1+{\tfrac{1}{a}}+b)}" alt="Mean for a Kumaraswamy's double bounded distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="\mathbb{E} \left[ X \right] = {b\Gamma(1+{\tfrac {1}{a}})\Gamma(b)}{\Gamma(1+{\tfrac{1}{a}}+b)}" data-equation="eq:kumaraswamy_mean">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/mean/docs/img/equation_kumaraswamy_mean.svg" alt="Mean for a Kumaraswamy's double bounded distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `a` is the first shape parameter, `b` the second shape parameter, and `Γ` denotes the [gamma function][gamma-function].
     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/kumaraswamy/mean' );
     54 ```
     55 
     56 #### mean( a, b )
     57 
     58 Returns the [expected value][mean] of a [Kumaraswamy's double bounded][kumaraswamy-distribution] distribution with first shape parameter `a` and second shape parameter `b`.
     59 
     60 ```javascript
     61 var v = mean( 1.5, 1.5 );
     62 // returns ~0.512
     63 
     64 v = mean( 4.0, 12.0 );
     65 // returns ~0.481
     66 
     67 v = mean( 2.0, 8.0 );
     68 // returns ~0.3
     69 ```
     70 
     71 If provided `NaN` as any argument, the function returns `NaN`.
     72 
     73 ```javascript
     74 var v = mean( NaN, 2.0 );
     75 // returns NaN
     76 
     77 v = mean( 2.0, NaN );
     78 // returns NaN
     79 ```
     80 
     81 If provided `a <= 0`, the function returns `NaN`.
     82 
     83 ```javascript
     84 var y = mean( -1.0, 2.0 );
     85 // returns NaN
     86 
     87 y = mean( 0.0, 2.0 );
     88 // returns NaN
     89 ```
     90 
     91 If provided `b <= 0`, the function returns `NaN`.
     92 
     93 ```javascript
     94 var y = mean( 2.0, -1.0 );
     95 // returns NaN
     96 
     97 y = mean( 2.0, 0.0 );
     98 // returns NaN
     99 ```
    100 
    101 </section>
    102 
    103 <!-- /.usage -->
    104 
    105 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    106 
    107 <section class="notes">
    108 
    109 </section>
    110 
    111 <!-- /.notes -->
    112 
    113 <!-- Package usage examples. -->
    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 mean = require( '@stdlib/stats/base/dists/kumaraswamy/mean' );
    124 
    125 var a;
    126 var b;
    127 var v;
    128 var i;
    129 
    130 for ( i = 0; i < 10; i++ ) {
    131     a = randu() * 10.0;
    132     b = randu() * 10.0;
    133     v = mean( a, b );
    134     console.log( 'a: %d, b: %d, E(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
    135 }
    136 ```
    137 
    138 </section>
    139 
    140 <!-- /.examples -->
    141 
    142 <!-- 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. -->
    143 
    144 <section class="references">
    145 
    146 </section>
    147 
    148 <!-- /.references -->
    149 
    150 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    151 
    152 <section class="links">
    153 
    154 [gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
    155 
    156 [kumaraswamy-distribution]: https://en.wikipedia.org/wiki/Kumaraswamy_distribution
    157 
    158 [mean]: https://en.wikipedia.org/wiki/Mean
    159 
    160 </section>
    161 
    162 <!-- /.links -->