time-to-botec

Benchmark sampling in different programming languages
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README.md (3982B)

      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
     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.
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     19 -->
     20 
     21 # Kurtosis
     22 
     23 > [Student's t][t-distribution] distribution [excess kurtosis][kurtosis].
     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 [excess kurtosis][kurtosis] for a [Student's t][t-distribution] random variable with degrees of freedom `ν` is
     30 
     31 <!-- <equation class="equation" label="eq:t_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = \begin{cases} \frac{6}{\nu-4} & \text{ for } \nu > 2 \\ \infty & \text{ for } 2 < \nu \le 4 \end{cases}" alt="Excess kurtosis for a Student's t distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = \begin{cases} \frac{6}{\nu-4} &amp; \text{ for } \nu &gt; 2 \\ \infty &amp; \text{ for } 2 &lt; \nu \le 4 \end{cases}" data-equation="eq:t_kurtosis">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/t/kurtosis/docs/img/equation_t_kurtosis.svg" alt="Excess kurtosis for a Student's t distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 For `ν` smaller than two, the kurtosis is not defined.
     41 
     42 </section>
     43 
     44 <!-- /.intro -->
     45 
     46 <!-- Package usage documentation. -->
     47 
     48 <section class="usage">
     49 
     50 ## Usage
     51 
     52 ```javascript
     53 var kurtosis = require( '@stdlib/stats/base/dists/t/kurtosis' );
     54 ```
     55 
     56 #### kurtosis( v )
     57 
     58 Returns the [excess kurtosis][kurtosis] of a [Student's t][t-distribution] distribution with degrees of freedom `v`.
     59 
     60 ```javascript
     61 var y = kurtosis( 9.0 );
     62 // returns 1.2
     63 
     64 y = kurtosis( 4.5 );
     65 // returns 12.0
     66 ```
     67 
     68 If provided `2 < v <= 4`, the function returns `infinity`.
     69 
     70 ```javascript
     71 var y = kurtosis( 3.5 );
     72 // returns Infinity
     73 
     74 y = kurtosis( 2.9 );
     75 // returns Infinity
     76 
     77 y = kurtosis( 4.0 );
     78 // returns Infinity
     79 ```
     80 
     81 If provided `v <= 2`, the function returns `NaN`.
     82 
     83 ```javascript
     84 var y = kurtosis( -1.0 );
     85 // returns NaN
     86 
     87 y = kurtosis( 0.8 );
     88 // returns NaN
     89 
     90 y = kurtosis( 2.0 );
     91 // returns NaN
     92 ```
     93 
     94 </section>
     95 
     96 <!-- /.usage -->
     97 
     98 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
     99 
    100 <section class="notes">
    101 
    102 </section>
    103 
    104 <!-- /.notes -->
    105 
    106 <!-- Package usage examples. -->
    107 
    108 <section class="examples">
    109 
    110 ## Examples
    111 
    112 <!-- eslint no-undef: "error" -->
    113 
    114 ```javascript
    115 var randu = require( '@stdlib/random/base/randu' );
    116 var round = require( '@stdlib/math/base/special/round' );
    117 var kurtosis = require( '@stdlib/stats/base/dists/t/kurtosis' );
    118 
    119 var v;
    120 var y;
    121 var i;
    122 
    123 for ( i = 0; i < 10; i++ ) {
    124     v = randu() * 20.0;
    125     y = kurtosis( v );
    126     console.log( 'v: %d, Kurt(X,v): %d', v.toFixed( 4 ), y.toFixed( 4 ) );
    127 }
    128 ```
    129 
    130 </section>
    131 
    132 <!-- /.examples -->
    133 
    134 <!-- 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. -->
    135 
    136 <section class="references">
    137 
    138 </section>
    139 
    140 <!-- /.references -->
    141 
    142 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    143 
    144 <section class="links">
    145 
    146 [t-distribution]: https://en.wikipedia.org/wiki/Student%27s_t-distribution
    147 
    148 [kurtosis]: https://en.wikipedia.org/wiki/Kurtosis
    149 
    150 </section>
    151 
    152 <!-- /.links -->