time-to-botec

Benchmark sampling in different programming languages
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README.md (4329B)

      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
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     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 > [Triangular][triangular-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 [triangular][triangular-distribution] random variable is
     30 
     31 <!-- <equation class="equation" label="eq:triangular_skewness" align="center" raw="\operatorname{skew}\left( X \right) = \frac{{\sqrt 2}(a\!+\!b\!-\!2c)(2a\!-\!b\!-\!c)(a\!-\!2b\!+\!c)}{5(a^{2}\!+\!b^{2}\!+\!c^{2}\!-\!ab\!-\!ac\!-\!bc)^{{\frac{3}{2}}}}" alt="Skewness for a triangular distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="\operatorname{skew}\left( X \right) = \frac{{\sqrt 2}(a\!+\!b\!-\!2c)(2a\!-\!b\!-\!c)(a\!-\!2b\!+\!c)}{5(a^{2}\!+\!b^{2}\!+\!c^{2}\!-\!ab\!-\!ac\!-\!bc)^{{\frac{3}{2}}}}" data-equation="eq:triangular_skewness">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@556e0ebc42f54244079cecc91c0883bb6c442244/lib/node_modules/@stdlib/stats/base/dists/triangular/skewness/docs/img/equation_triangular_skewness.svg" alt="Skewness for a triangular distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `a` is the lower limit, `b` is the upper limit and `c` is the mode.
     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/triangular/skewness' );
     54 ```
     55 
     56 #### skewness( a, b, c )
     57 
     58 Returns the [skewness][skewness] of a [triangular][triangular-distribution] distribution with minimum support `a`, maximum support`b`, and mode `c`.
     59 
     60 ```javascript
     61 var v = skewness( 0.0, 1.0, 0.8 );
     62 // returns ~-0.476
     63 
     64 v = skewness( 4.0, 12.0, 5.0 );
     65 // returns ~0.532
     66 
     67 v = skewness( 2.0, 8.0, 5.0 );
     68 // returns 0.0
     69 ```
     70 
     71 If provided `NaN` as any argument, the function returns `NaN`.
     72 
     73 ```javascript
     74 var v = skewness( NaN, 4.0, 2.0 );
     75 // returns NaN
     76 
     77 v = skewness( 0.0, NaN, 2.0 );
     78 // returns NaN
     79 
     80 v = skewness( 0.0, 4.0, NaN );
     81 // returns NaN
     82 ```
     83 
     84 If provided parameters not satisfying `a <= c <= b`, the function returns `NaN`.
     85 
     86 ```javascript
     87 var y = skewness( 1.0, 0.0, 1.5 );
     88 // returns NaN
     89 
     90 y = skewness( 0.0, 1.0, -1.0 );
     91 // returns NaN
     92 
     93 y = skewness( 0.0, -1.0, 0.5 );
     94 // returns NaN
     95 ```
     96 
     97 </section>
     98 
     99 <!-- /.usage -->
    100 
    101 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    102 
    103 <section class="notes">
    104 
    105 </section>
    106 
    107 <!-- /.notes -->
    108 
    109 <!-- Package usage examples. -->
    110 
    111 <section class="examples">
    112 
    113 ## Examples
    114 
    115 <!-- eslint no-undef: "error" -->
    116 
    117 ```javascript
    118 var randu = require( '@stdlib/random/base/randu' );
    119 var skewness = require( '@stdlib/stats/base/dists/triangular/skewness' );
    120 
    121 var a;
    122 var b;
    123 var c;
    124 var v;
    125 var i;
    126 
    127 for ( i = 0; i < 10; i++ ) {
    128     a = ( randu()*10.0 );
    129     b = ( randu()*10.0 ) + a;
    130     c = ( randu()*( b-a ) ) + a;
    131     v = skewness( a, b, c );
    132     console.log( 'a: %d, b: %d, c: %d, skew(X;a,b,c): %d', a.toFixed( 4 ), b.toFixed( 4 ), c.toFixed( 4 ), v.toFixed( 4 ) );
    133 }
    134 ```
    135 
    136 </section>
    137 
    138 <!-- /.examples -->
    139 
    140 <!-- 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. -->
    141 
    142 <section class="references">
    143 
    144 </section>
    145 
    146 <!-- /.references -->
    147 
    148 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    149 
    150 <section class="links">
    151 
    152 [triangular-distribution]: https://en.wikipedia.org/wiki/Triangular_distribution
    153 
    154 [skewness]: https://en.wikipedia.org/wiki/Skewness
    155 
    156 </section>
    157 
    158 <!-- /.links -->