time-to-botec

Benchmark sampling in different programming languages
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README.md (4091B)

      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.
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     19 -->
     20 
     21 # Skewness
     22 
     23 > [Erlang][erlang-distribution] distribution [skewness][skewness].
     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 [skewness][skewness] for an [Erlang][erlang-distribution] random variable with shape `k` and rate `λ` is
     30 
     31 <!-- <equation class="equation" label="eq:erlang_skewness" align="center" raw="\operatorname{skew}\left( X \right) = \frac{2}{\sqrt{k}}" alt="Skewness for an Erlang distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="\operatorname{skew}\left( X \right) = \frac{2}{\sqrt{k}}" data-equation="eq:erlang_skewness">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/erlang/skewness/docs/img/equation_erlang_skewness.svg" alt="Skewness for an Erlang distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <!-- Package usage documentation. -->
     45 
     46 <section class="usage">
     47 
     48 ## Usage
     49 
     50 ```javascript
     51 var skewness = require( '@stdlib/stats/base/dists/erlang/skewness' );
     52 ```
     53 
     54 #### skewness( k, lambda )
     55 
     56 Returns the [skewness][skewness] of an [Erlang][erlang-distribution] distribution with parameters `k` (shape parameter) and `lambda` (rate parameter).
     57 
     58 ```javascript
     59 var v = skewness( 1, 1.0 );
     60 // returns 2.0
     61 
     62 v = skewness( 4, 12.0 );
     63 // returns 1.0
     64 
     65 v = skewness( 8, 2.0 );
     66 // returns ~0.707
     67 ```
     68 
     69 If provided `NaN` as any argument, the function returns `NaN`.
     70 
     71 ```javascript
     72 var v = skewness( NaN, 2.0 );
     73 // returns NaN
     74 
     75 v = skewness( 2.0, NaN );
     76 // returns NaN
     77 ```
     78 
     79 If not provided a positive integer for `k`, the function returns `NaN`.
     80 
     81 ```javascript
     82 var v = skewness( 1.8, 1.0 );
     83 // returns NaN
     84 
     85 v = skewness( -1.0, 1.0 );
     86 // returns NaN
     87 ```
     88 
     89 If provided `lambda <= 0`, the function returns `NaN`.
     90 
     91 ```javascript
     92 var v = skewness( 2, 0.0 );
     93 // returns NaN
     94 
     95 v = skewness( 2, -1.0 );
     96 // returns NaN
     97 ```
     98 
     99 </section>
    100 
    101 <!-- /.usage -->
    102 
    103 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    104 
    105 <section class="notes">
    106 
    107 </section>
    108 
    109 <!-- /.notes -->
    110 
    111 <!-- Package usage examples. -->
    112 
    113 <section class="examples">
    114 
    115 ## Examples
    116 
    117 <!-- eslint no-undef: "error" -->
    118 
    119 ```javascript
    120 var randu = require( '@stdlib/random/base/randu' );
    121 var round = require( '@stdlib/math/base/special/round' );
    122 var EPS = require( '@stdlib/constants/float64/eps' );
    123 var skewness = require( '@stdlib/stats/base/dists/erlang/skewness' );
    124 
    125 var lambda;
    126 var k;
    127 var v;
    128 var i;
    129 
    130 for ( i = 0; i < 10; i++ ) {
    131     k = round( randu()*10.0 );
    132     lambda = ( randu()*10.0 ) + EPS;
    133     v = skewness( k, lambda );
    134     console.log( 'k: %d, λ: %d, skew(X;k,λ): %d', k.toFixed( 4 ), lambda.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 [erlang-distribution]: https://en.wikipedia.org/wiki/Erlang_distribution
    155 
    156 [skewness]: https://en.wikipedia.org/wiki/Skewness
    157 
    158 </section>
    159 
    160 <!-- /.links -->