time-to-botec

Benchmark sampling in different programming languages
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README.md (3984B)

      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 # Cumulative Distribution Function
     22 
     23 > [Poisson][poisson-distribution] distribution [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for a [Poisson][poisson-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:poisson_cdf" align="center" raw="F(x;\lambda) = \begin{cases} 0 & \text{ for } x \le 0 \\ e^{-\lambda} \sum_{i=0}^{\lfloor x\rfloor} \frac{\lambda^i}{i!} & \text{ for } x > 0 \end{cases}" alt="Cumulative distribution function for a Poisson distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F(x;\lambda) = \begin{cases} 0 &amp; \text{ for } x \le 0 \\ e^{-\lambda} \sum_{i=0}^{\lfloor x\rfloor} \frac{\lambda^i}{i!} &amp; \text{ for } x &gt; 0 \end{cases}" data-equation="eq:poisson_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/poisson/cdf/docs/img/equation_poisson_cdf.svg" alt="Cumulative distribution function for a Poisson distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `lambda` is the mean parameter. Internally, the module evaluates the CDF by evaluating the upper regularized gamma function at input values `lambda` and `floor( x ) + 1`.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var cdf = require( '@stdlib/stats/base/dists/poisson/cdf' );
     50 ```
     51 
     52 #### cdf( x, lambda )
     53 
     54 Evaluates the [cumulative distribution function][cdf] for a [Poisson][poisson-distribution] distribution with mean parameter `lambda`.
     55 
     56 ```javascript
     57 var y = cdf( 2.0, 0.5 );
     58 // returns ~0.986
     59 
     60 y = cdf( 2.0, 10.0 );
     61 // returns ~0.003
     62 
     63 y = cdf( -1.0, 4.0 );
     64 // returns 0.0
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = cdf( NaN, 1.0 );
     71 // returns NaN
     72 
     73 y = cdf( 0.0, NaN );
     74 // returns NaN
     75 ```
     76 
     77 If provided `lambda < 0`, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = cdf( 2.0, -1.0 );
     81 // returns NaN
     82 ```
     83 
     84 If provided `lambda = 0`, the function evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at `0`.
     85 
     86 ```javascript
     87 var y = cdf( -2.0, 0.0 );
     88 // returns 0.0
     89 
     90 y = cdf( 0.0, 0.0 );
     91 // returns 1.0
     92 
     93 y = cdf( 10.0, 0.0 );
     94 // returns 1.0
     95 ```
     96 
     97 #### cdf.factory( lambda )
     98 
     99 Returns a function for evaluating the [cumulative distribution function][cdf] of a [Poisson][poisson-distribution] distribution with mean parameter `lambda`.
    100 
    101 ```javascript
    102 var mycdf = cdf.factory( 5.0 );
    103 var y = mycdf( 3.0 );
    104 // returns ~0.265
    105 
    106 y = mycdf( 8.0 );
    107 // returns ~0.932
    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 cdf = require( '@stdlib/stats/base/dists/poisson/cdf' );
    123 
    124 var lambda;
    125 var x;
    126 var y;
    127 var i;
    128 
    129 for ( i = 0; i < 10; i++ ) {
    130     x = randu() * 10.0;
    131     lambda = randu() * 10.0;
    132     y = cdf( x, lambda );
    133     console.log( 'x: %d, λ: %d, F(x;λ): %d', x.toFixed( 4 ), lambda.toFixed( 4 ), y.toFixed( 4 ) );
    134 }
    135 ```
    136 
    137 </section>
    138 
    139 <!-- /.examples -->
    140 
    141 <section class="links">
    142 
    143 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    144 
    145 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    146 
    147 [poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution
    148 
    149 </section>
    150 
    151 <!-- /.links -->