time-to-botec

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

README.md (3837B)

      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 # Mode
     22 
     23 > [Bernoulli][bernoulli-distribution] distribution [mode][mode].
     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 [mode][mode] for a [Bernoulli][bernoulli-distribution] random variable is
     30 
     31 <!-- <equation class="equation" label="eq:bernoulli_mode" align="center" raw="\operatorname{Mode}\left( X \right) = \begin{cases} 0 & \text{if } p < 1/2 \\ 0, 1 &\text{if } p = 1/2 \\ 1 & \text{if } p > 1/2 \end{cases}" alt="Mode for a Bernoulli distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="\operatorname{Mode}\left( X \right) = \begin{cases} 0 &amp; \text{if } p &lt; 1/2 \\ 0, 1 &amp;\text{if } p = 1/2 \\ 1 &amp; \text{if } p &gt; 1/2 \end{cases}" data-equation="eq:bernoulli_mode">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@e1fbdee688c5409e4cc6b0cd06d90b1cd2abd67c/lib/node_modules/@stdlib/stats/base/dists/bernoulli/mode/docs/img/equation_bernoulli_mode.svg" alt="Mode for a Bernoulli distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `p` is the success probability.
     41 
     42 </section>
     43 
     44 <!-- /.intro -->
     45 
     46 <!-- Package usage documentation. -->
     47 
     48 <section class="usage">
     49 
     50 ## Usage
     51 
     52 ```javascript
     53 var mode = require( '@stdlib/stats/base/dists/bernoulli/mode' );
     54 ```
     55 
     56 #### mode( p )
     57 
     58 Returns the [mode][mode] of a [Bernoulli][bernoulli-distribution] distribution with success probability `p`.
     59 
     60 ```javascript
     61 var v = mode( 0.1 );
     62 // returns 0
     63 
     64 v = mode( 0.5 );
     65 // returns 0
     66 
     67 v = mode( 0.8 );
     68 // returns 1
     69 ```
     70 
     71 If provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.
     72 
     73 ```javascript
     74 var v = mode( NaN );
     75 // returns NaN
     76 
     77 v = mode( 1.5 );
     78 // returns NaN
     79 
     80 v = mode( -1.0 );
     81 // returns NaN
     82 ```
     83 
     84 </section>
     85 
     86 <!-- /.usage -->
     87 
     88 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
     89 
     90 <section class="notes">
     91 
     92 ## Notes
     93 
     94 -   For `p = 0.5`, the mode is either `0` or `1`. This implementation returns `0` for `p = 0.5`.
     95 
     96 </section>
     97 
     98 <!-- /.notes -->
     99 
    100 <!-- Package usage examples. -->
    101 
    102 <section class="examples">
    103 
    104 ## Examples
    105 
    106 <!-- eslint no-undef: "error" -->
    107 
    108 ```javascript
    109 var randu = require( '@stdlib/random/base/randu' );
    110 var round = require( '@stdlib/math/base/special/round' );
    111 var mode = require( '@stdlib/stats/base/dists/bernoulli/mode' );
    112 
    113 var v;
    114 var i;
    115 var p;
    116 
    117 for ( i = 0; i < 10; i++ ) {
    118     p = randu();
    119     v = mode( p );
    120     console.log( 'p: %d, Mode(X;p): %d', p.toFixed( 4 ), v.toFixed( 4 ) );
    121 }
    122 ```
    123 
    124 </section>
    125 
    126 <!-- /.examples -->
    127 
    128 <!-- 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. -->
    129 
    130 <section class="references">
    131 
    132 </section>
    133 
    134 <!-- /.references -->
    135 
    136 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    137 
    138 <section class="links">
    139 
    140 [bernoulli-distribution]: https://en.wikipedia.org/wiki/Bernoulli_distribution
    141 
    142 [mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29
    143 
    144 </section>
    145 
    146 <!-- /.links -->