time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

README.md (4262B)

      1 <!--
      2 
      3 @license Apache-2.0
      4 
      5 Copyright (c) 2018 The Stdlib Authors.
      6 
      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
     10 
     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.
     18 
     19 -->
     20 
     21 # Skewness
     22 
     23 > [Negative binomial][negative-binomial-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 a [negative binomial][negative-binomial-distribution] random variable is
     30 
     31 <!-- <equation class="equation" label="eq:negative_binomial_skewness" align="center" raw="\operatorname{skew}\left( X \right) = \frac{1+p}{\sqrt{pr}}" alt="Skewness for a negative binomial distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="\operatorname{skew}\left( X \right) = \frac{1+p}{\sqrt{pr}}" data-equation="eq:negative_binomial_skewness">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/negative-binomial/skewness/docs/img/equation_negative_binomial_skewness.svg" alt="Skewness for a negative binomial distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `r` is the number of successes until experiment is stopped and `p` is the success probability in each trial. The random variable `X` denotes the number of failures until the `r` success is reached. 
     41 
     42 </section>
     43 
     44 <!-- /.intro -->
     45 
     46 <!-- Package usage documentation. -->
     47 
     48 <section class="usage">
     49 
     50 ## Usage
     51 
     52 ```javascript
     53 var skewness = require( '@stdlib/stats/base/dists/negative-binomial/skewness' );
     54 ```
     55 
     56 #### skewness( r, p )
     57 
     58 Returns the [skewness][skewness] of a [negative binomial][negative-binomial-distribution] distribution with parameters `r` (number of successes until experiment is stopped) and `p` (success probability).
     59 
     60 ```javascript
     61 var v = skewness( 100, 0.2 );
     62 // returns ~0.201
     63 
     64 v = skewness( 50, 0.5 );
     65 // returns ~0.3
     66 ```
     67 
     68 If provided `NaN` as any argument, the function returns `NaN`.
     69 
     70 ```javascript
     71 var v = skewness( NaN, 0.5 );
     72 // returns NaN
     73 
     74 v = skewness( 20, NaN );
     75 // returns NaN
     76 ```
     77 
     78 If provided a `r` which is not a positive number, the function returns `NaN`.
     79 
     80 ```javascript
     81 var v = skewness( -2.0, 0.5 );
     82 // returns NaN
     83 ```
     84 
     85 If provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.
     86 
     87 ```javascript
     88 var v = skewness( 20, -1.0 );
     89 // returns NaN
     90 
     91 v = skewness( 20, 1.5 );
     92 // returns NaN
     93 ```
     94 
     95 </section>
     96 
     97 <!-- /.usage -->
     98 
     99 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    100 
    101 <section class="notes">
    102 
    103 </section>
    104 
    105 <!-- /.notes -->
    106 
    107 <!-- Package usage examples. -->
    108 
    109 <section class="examples">
    110 
    111 ## Examples
    112 
    113 <!-- eslint no-undef: "error" -->
    114 
    115 ```javascript
    116 var randu = require( '@stdlib/random/base/randu' );
    117 var skewness = require( '@stdlib/stats/base/dists/negative-binomial/skewness' );
    118 
    119 var v;
    120 var i;
    121 var r;
    122 var p;
    123 
    124 for ( i = 0; i < 10; i++ ) {
    125     r = randu() * 100;
    126     p = randu();
    127     v = skewness( r, p );
    128     console.log( 'r: %d, p: %d, skew(X;r,p): %d', r, p.toFixed( 4 ), v.toFixed( 4 ) );
    129 }
    130 ```
    131 
    132 </section>
    133 
    134 <!-- /.examples -->
    135 
    136 <!-- 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. -->
    137 
    138 <section class="references">
    139 
    140 </section>
    141 
    142 <!-- /.references -->
    143 
    144 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    145 
    146 <section class="links">
    147 
    148 [negative-binomial-distribution]: https://en.wikipedia.org/wiki/Negative_binomial_distribution
    149 
    150 [skewness]: https://en.wikipedia.org/wiki/Skewness
    151 
    152 </section>
    153 
    154 <!-- /.links -->