time-to-botec

Benchmark sampling in different programming languages
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README.md (3593B)

      1 <!--
      2 
      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
     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.
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     19 -->
     20 
     21 # Cumulative Distribution Function
     22 
     23 > [Gumbel][gumbel-distribution] distribution [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for a [Gumbel][gumbel-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:gumbel_cdf" align="center" raw="F\left( x; \mu, \beta \right ) = e^{{-e^{{-(x-\mu )/\beta }}}}" alt="Cumulative distribution function for a Gumbel distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F\left( x; \mu, \beta \right ) = e^{{-e^{{-(x-\mu )/\beta }}}}" data-equation="eq:gumbel_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/gumbel/cdf/docs/img/equation_gumbel_cdf.svg" alt="Cumulative distribution function for a Gumbel distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `mu` is the location parameter and `beta > 0` is the scale 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/gumbel/cdf' );
     50 ```
     51 
     52 #### cdf( x, mu, beta )
     53 
     54 Evaluates the [cumulative distribution function][cdf] (CDF) for a [Gumbel][gumbel-distribution] distribution with parameters `mu` (location parameter) and `beta` (scale parameter).
     55 
     56 ```javascript
     57 var y = cdf( 10.0, 0.0, 3.0 );
     58 // returns ~0.965
     59 
     60 y = cdf( -2.0, 0.0, 3.0 );
     61 // returns ~0.143
     62 
     63 y = cdf( 0.0, 0.0, 1.0 );
     64 // returns ~0.368
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = cdf( NaN, 0.0, 1.0 );
     71 // returns NaN
     72 
     73 y = cdf( 0.0, NaN, 1.0 );
     74 // returns NaN
     75 
     76 y = cdf( 0.0, 0.0, NaN );
     77 // returns NaN
     78 ```
     79 
     80 If provided `beta <= 0`, the function returns `NaN`.
     81 
     82 ```javascript
     83 var y = cdf( 2.0, 0.0, -1.0 );
     84 // returns NaN
     85 
     86 y = cdf( 2.0, 0.0, 0.0 );
     87 // returns NaN
     88 ```
     89 
     90 #### cdf.factory( mu, beta )
     91 
     92 Returns a function for evaluating the [cumulative distribution function][cdf] of a [Gumbel][gumbel-distribution] distribution with parameters `mu` (location parameter) and `beta` (scale parameter).
     93 
     94 ```javascript
     95 var mycdf = cdf.factory( 0.0, 3.0 );
     96 
     97 var y = mycdf( 10.0 );
     98 // returns ~0.965
     99 
    100 y = mycdf( -2.0 );
    101 // returns ~0.143
    102 ```
    103 
    104 </section>
    105 
    106 <!-- /.usage -->
    107 
    108 <section class="examples">
    109 
    110 ## Examples
    111 
    112 <!-- eslint no-undef: "error" -->
    113 
    114 ```javascript
    115 var randu = require( '@stdlib/random/base/randu' );
    116 var cdf = require( '@stdlib/stats/base/dists/gumbel/cdf' );
    117 
    118 var beta;
    119 var mu;
    120 var x;
    121 var y;
    122 var i;
    123 
    124 for ( i = 0; i < 100; i++ ) {
    125     x = randu() * 10.0;
    126     mu = randu() * 10.0;
    127     beta = randu() * 10.0;
    128     y = cdf( x, mu, beta );
    129     console.log( 'x: %d, µ: %d, β: %d, F(x;µ,β): %d', x.toFixed( 4 ), mu.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
    130 }
    131 ```
    132 
    133 </section>
    134 
    135 <!-- /.examples -->
    136 
    137 <section class="links">
    138 
    139 [gumbel-distribution]: https://en.wikipedia.org/wiki/Gumbel_distribution
    140 
    141 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    142 
    143 </section>
    144 
    145 <!-- /.links -->