time-to-botec

Benchmark sampling in different programming languages
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README.md (3561B)

      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 # Probability Mass Function
     22 
     23 > [Bernoulli][bernoulli-distribution] distribution [probability mass function][pmf] (PMF).
     24 
     25 <section class="intro">
     26 
     27 The [probability mass function][pmf] (PMF) for a [Bernoulli][bernoulli-distribution] random variable is defined as
     28 
     29 <!-- <equation class="equation" label="eq:bernoulli_pmf" align="center" raw="\Pr(X = x) = \begin{cases} 1-p & \text{ for } x = 0 \\ p & \text{ for } x = 1 \\ 0 & \text{ otherwise } \end{cases}" alt="Probability mass function (PMF) for a Bernoulli distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="\Pr(X = x) = \begin{cases} 1-p &amp; \text{ for } x = 0 \\ p &amp; \text{ for } x = 1 \\ 0 &amp; \text{ otherwise } \end{cases}" data-equation="eq:bernoulli_pmf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/bernoulli/pmf/docs/img/equation_bernoulli_pmf.svg" alt="Probability mass function (PMF) for a Bernoulli distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `0 <= p <= 1` is the success probability.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var pmf = require( '@stdlib/stats/base/dists/bernoulli/pmf' );
     50 ```
     51 
     52 #### pmf( x, p )
     53 
     54 Evaluates the [probability mass function][pmf] (PMF) of a [Bernoulli][bernoulli-distribution] distribution with success probability `0 <= p <= 1`.
     55 
     56 ```javascript
     57 var y = pmf( 1.0, 0.3 );
     58 // returns 0.3
     59 
     60 y = pmf( 0.0, 0.3 );
     61 // returns 0.7
     62 
     63 y = pmf( -1.0, 0.5 );
     64 // returns 0.0
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = pmf( NaN, 0.0 );
     71 // returns NaN
     72 
     73 y = pmf( 0.0, NaN );
     74 // returns NaN
     75 ```
     76 
     77 If provided a success probability `p` outside of the interval `[0,1]`, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = pmf( 0.0, -1.0 );
     81 // returns NaN
     82 
     83 y = pmf( 0.0, 1.5 );
     84 // returns NaN
     85 ```
     86 
     87 #### pmf.factory( p )
     88 
     89 Returns a function for evaluating the [probability mass function][pmf] (PMF) of a [Bernoulli][bernoulli-distribution] distribution with success probability `0 <= p <= 1`.
     90 
     91 ```javascript
     92 var mypmf = pmf.factory( 0.8 );
     93 var y = mypmf( 0.0 );
     94 // returns 0.2
     95 
     96 y = mypmf( 0.5 );
     97 // returns 0.0
     98 ```
     99 
    100 </section>
    101 
    102 <!-- /.usage -->
    103 
    104 <section class="examples">
    105 
    106 ## Examples
    107 
    108 <!-- eslint no-undef: "error" -->
    109 
    110 ```javascript
    111 var randu = require( '@stdlib/random/base/randu' );
    112 var round = require( '@stdlib/math/base/special/round' );
    113 var pmf = require( '@stdlib/stats/base/dists/bernoulli/pmf' );
    114 
    115 var p;
    116 var x;
    117 var y;
    118 var i;
    119 
    120 for ( i = 0; i < 10; i++ ) {
    121     x = round( randu() * 2.0 );
    122     p = randu();
    123     y = pmf( x, p );
    124     console.log( 'x: %d, p: %d, P( X = x; p ): %d', x, p.toFixed( 4 ), y.toFixed( 4 ) );
    125 }
    126 ```
    127 
    128 </section>
    129 
    130 <!-- /.examples -->
    131 
    132 <section class="links">
    133 
    134 [bernoulli-distribution]: https://en.wikipedia.org/wiki/Bernoulli_distribution
    135 
    136 [pmf]: https://en.wikipedia.org/wiki/Probability_mass_function
    137 
    138 </section>
    139 
    140 <!-- /.links -->