time-to-botec

Benchmark sampling in different programming languages
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README.md (3353B)

      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 # Cumulative Distribution Function
     22 
     23 > [Exponential][exponential-distribution] distribution [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for an [exponential][exponential-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:exponential_cdf" align="center" raw="F(x;\lambda) = \begin{cases} 1-e^{-\lambda x} & x \ge 0 \\ 0 & x < 0 \end{cases}" alt="Cumulative distribution function for an exponential distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F(x;\lambda) = \begin{cases} 1-e^{-\lambda x} &amp; x \ge 0 \\ 0 &amp; x &lt; 0 \end{cases}" data-equation="eq:exponential_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/exponential/cdf/docs/img/equation_exponential_cdf.svg" alt="Cumulative distribution function for an exponential distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `λ` is the rate parameter.
     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/exponential/cdf' );
     50 ```
     51 
     52 #### cdf( x, lambda )
     53 
     54 Evaluates the [cumulative distribution function][cdf] for an [exponential][exponential-distribution] distribution with rate parameter `lambda`.
     55 
     56 ```javascript
     57 var y = cdf( 2.0, 0.3 );
     58 // returns ~0.451
     59 
     60 y = cdf( 10.0, 0.3 );
     61 // returns ~0.95
     62 ```
     63 
     64 If provided `NaN` as any argument, the function returns `NaN`.
     65 
     66 ```javascript
     67 var y = cdf( NaN, 0.0 );
     68 // returns NaN
     69 
     70 y = cdf( 0.0, NaN );
     71 // returns NaN
     72 ```
     73 
     74 If provided `lambda < 0`, the function returns `NaN`.
     75 
     76 ```javascript
     77 var y = cdf( 2.0, -1.0 );
     78 // returns NaN
     79 ```
     80 
     81 #### cdf.factory( lambda )
     82 
     83 Returns a function for evaluating the [cumulative distribution function (CDF)][cdf] for an exponential distribution with rate parameter `lambda`.
     84 
     85 ```javascript
     86 var mycdf = cdf.factory( 0.1 );
     87 
     88 var y = mycdf( 8.0 );
     89 // returns ~0.551
     90 
     91 y = mycdf( 2.0 );
     92 // returns ~0.181
     93 
     94 y = mycdf( 0.0 );
     95 // returns 0.0
     96 ```
     97 
     98 </section>
     99 
    100 <!-- /.usage -->
    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 cdf = require( '@stdlib/stats/base/dists/exponential/cdf' );
    111 
    112 var lambda;
    113 var x;
    114 var y;
    115 var i;
    116 
    117 for ( i = 0; i < 10; i++ ) {
    118     x = randu() * 10.0;
    119     lambda = randu() * 10.0;
    120     y = cdf( x, lambda );
    121     console.log( 'x: %d, λ: %d, F(x;λ): %d', x, lambda, y );
    122 }
    123 ```
    124 
    125 </section>
    126 
    127 <!-- /.examples -->
    128 
    129 <section class="links">
    130 
    131 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    132 
    133 [exponential-distribution]: https://en.wikipedia.org/wiki/Exponential_distribution
    134 
    135 </section>
    136 
    137 <!-- /.links -->