time-to-botec

Benchmark sampling in different programming languages
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README.md (3885B)

      1 <!--
      2 
      3 @license Apache-2.0
      4 
      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.
     18 
     19 -->
     20 
     21 # Probability Mass Function
     22 
     23 > [Poisson][poisson-distribution] distribution [probability mass function][pmf] (PMF).
     24 
     25 <section class="intro">
     26 
     27 The [probability mass function][pmf] (PMF) for a [Poisson][poisson-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:poisson_pmf" align="center" raw="f(x;\lambda)=P(X=x;\lambda)=\begin{cases} \tfrac{\lambda^x}{x!}e^{-\lambda} & \text{ for } x = 0,1,2,\ldots \\ 0 & \text{ otherwise} \end{cases}" alt="Probability mass function (PMF) for a Poisson distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="f(x;\lambda)=P(X=x;\lambda)=\begin{cases} \tfrac{\lambda^x}{x!}e^{-\lambda} &amp; \text{ for } x = 0,1,2,\ldots \\ 0 &amp; \text{ otherwise} \end{cases}" data-equation="eq:poisson_pmf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/poisson/pmf/docs/img/equation_poisson_pmf.svg" alt="Probability mass function (PMF) for a Poisson distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `lambda > 0` is the mean parameter.
     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/poisson/pmf' );
     50 ```
     51 
     52 #### pmf( x, lambda )
     53 
     54 Evaluates the [probability mass function][pmf] (PMF) of a [Poisson][poisson-distribution] distribution with mean parameter `lambda`.
     55 
     56 ```javascript
     57 var y = pmf( 4.0, 3.0 );
     58 // returns ~0.168
     59 
     60 y = pmf( 1.0, 3.0 );
     61 // returns ~0.149
     62 
     63 y = pmf( -1.0, 2.0 );
     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, 2.0 );
     71 // returns NaN
     72 
     73 y = pmf( 0.0, NaN );
     74 // returns NaN
     75 ```
     76 
     77 If provided a negative mean parameter `lambda`, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = pmf( 2.0, -1.0 );
     81 // returns NaN
     82 
     83 y = pmf( 4.0, -2.0 );
     84 // returns NaN
     85 ```
     86 
     87 If provided `lambda = 0`, the function evaluates the [PMF][pmf] of a [degenerate distribution][degenerate-distribution] centered at `0.0`.
     88 
     89 ```javascript
     90 var y = pmf( 2.0, 0.0 );
     91 // returns 0.0
     92 
     93 y = pmf( 0.0, 0.0 );
     94 // returns 1.0
     95 ```
     96 
     97 #### pmf.factory( lambda )
     98 
     99 Returns a function for evaluating the [probability mass function][pmf] (PMF) of a [Poisson][poisson-distribution] distribution with mean parameter `lambda`.
    100 
    101 ```javascript
    102 var mypmf = pmf.factory( 1.0 );
    103 var y = mypmf( 3.0 );
    104 // returns ~0.061
    105 
    106 y = mypmf( 1.0 );
    107 // returns ~0.368
    108 ```
    109 
    110 </section>
    111 
    112 <!-- /.usage -->
    113 
    114 <section class="examples">
    115 
    116 ## Examples
    117 
    118 <!-- eslint no-undef: "error" -->
    119 
    120 ```javascript
    121 var randu = require( '@stdlib/random/base/randu' );
    122 var round = require( '@stdlib/math/base/special/round' );
    123 var pmf = require( '@stdlib/stats/base/dists/poisson/pmf' );
    124 
    125 var lambda;
    126 var x;
    127 var y;
    128 var i;
    129 
    130 for ( i = 0; i < 10; i++ ) {
    131     x = round( randu() * 10.0 );
    132     lambda = randu() * 10.0;
    133     y = pmf( x, lambda );
    134     console.log( 'x: %d, λ: %d, P(X=x;λ): %d', x, lambda.toFixed( 4 ), y.toFixed( 4 ) );
    135 }
    136 ```
    137 
    138 </section>
    139 
    140 <!-- /.examples -->
    141 
    142 <section class="links">
    143 
    144 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    145 
    146 [poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution
    147 
    148 [pmf]: https://en.wikipedia.org/wiki/Probability_mass_function
    149 
    150 </section>
    151 
    152 <!-- /.links -->