time-to-botec

Benchmark sampling in different programming languages
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README.md (4058B)

      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 > [Fréchet][frechet-distribution] distribution [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for a [Fréchet][frechet-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:frechet_cdf" align="center" raw="F\left( x; \mu, \beta \right ) = e^{{-({\frac{x-m}{s}})^{{-\alpha }}}}" alt="Cumulative distribution function for a Fréchet distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F\left( x; \mu, \beta \right ) = e^{{-({\frac{x-m}{s}})^{{-\alpha }}}}" data-equation="eq:frechet_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/frechet/cdf/docs/img/equation_frechet_cdf.svg" alt="Cumulative distribution function for a Fréchet distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `alpha > 0` is the shape, `s > 0` the scale, and `m` the location 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/frechet/cdf' );
     50 ```
     51 
     52 #### cdf( x, alpha, s, m )
     53 
     54 Evaluates the [cumulative distribution function][cdf] (CDF) for a [Fréchet][frechet-distribution] distribution with shape `alpha`, scale `s`, and location `m` at a value `x`.
     55 
     56 ```javascript
     57 var y = cdf( 10.0, 2.0, 3.0, 5.0 );
     58 // returns ~0.698
     59 
     60 y = cdf( -3.0, 1.0, 2.0, -4.0 );
     61 // returns ~0.135
     62 
     63 y = cdf( 0.0, 2.0, 1.0, -1.0 );
     64 // returns ~0.368
     65 ```
     66 
     67 If provided `x <= m`, the function returns `0`.
     68 
     69 ```javascript
     70 var y = cdf( -2.0, 2.0, 1.0, -1.0 );
     71 // returns 0.0
     72 ```
     73 
     74 If provided `NaN` as any argument, the function returns `NaN`.
     75 
     76 ```javascript
     77 var y = cdf( NaN, 1.0, 1.0, 0.0 );
     78 // returns NaN
     79 
     80 y = cdf( 0.0, NaN, 1.0, 0.0 );
     81 // returns NaN
     82 
     83 y = cdf( 0.0, 1.0, NaN, 0.0);
     84 // returns NaN
     85 
     86 y = cdf( 0.0, 1.0, 1.0, NaN );
     87 // returns NaN
     88 ```
     89 
     90 If provided `alpha <= 0`, the function returns `NaN`.
     91 
     92 ```javascript
     93 var y = cdf( 2.0, -0.1, 1.0, 1.0 );
     94 // returns NaN
     95 
     96 y = cdf( 2.0, 0.0, 1.0, 1.0 );
     97 // returns NaN
     98 ```
     99 
    100 If provided `s <= 0`, the function returns `NaN`.
    101 
    102 ```javascript
    103 var y = cdf( 2.0, 1.0, -1.0, 1.0 );
    104 // returns NaN
    105 
    106 y = cdf( 2.0, 1.0, 0.0, 1.0 );
    107 // returns NaN
    108 ```
    109 
    110 #### cdf.factory( alpha, s, m )
    111 
    112 Returns a function for evaluating the [cumulative distribution function][cdf] of a [Fréchet][frechet-distribution] distribution with shape `alpha`, scale `s`, and location `m`.
    113 
    114 ```javascript
    115 var mycdf = cdf.factory( 3.0, 3.0, 5.0 );
    116 
    117 var y = mycdf( 10.0 );
    118 // returns ~0.806
    119 
    120 y = mycdf( 7.0 );
    121 // returns ~0.034
    122 ```
    123 
    124 </section>
    125 
    126 <!-- /.usage -->
    127 
    128 <section class="examples">
    129 
    130 ## Examples
    131 
    132 <!-- eslint no-undef: "error" -->
    133 
    134 ```javascript
    135 var randu = require( '@stdlib/random/base/randu' );
    136 var cdf = require( '@stdlib/stats/base/dists/frechet/cdf' );
    137 
    138 var alpha;
    139 var m;
    140 var s;
    141 var x;
    142 var y;
    143 var i;
    144 
    145 for ( i = 0; i < 100; i++ ) {
    146     alpha = randu() * 10.0;
    147     x = randu() * 10.0;
    148     s = randu() * 10.0;
    149     m = randu() * 10.0;
    150     y = cdf( x, alpha, s, m );
    151     console.log( 'x: %d, α: %d, s: %d, m: %d, F(x;α,s,m): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
    152 }
    153 ```
    154 
    155 </section>
    156 
    157 <!-- /.examples -->
    158 
    159 <section class="links">
    160 
    161 [frechet-distribution]: https://en.wikipedia.org/wiki/Fr%C3%A9chet_distribution
    162 
    163 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    164 
    165 </section>
    166 
    167 <!-- /.links -->