time-to-botec

Benchmark sampling in different programming languages
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README.md (3801B)

      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 > [Normal][normal-distribution] distribution [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for a [normal][normal-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:normal_cdf" align="center" raw="center" data-raw-text="F(x;\mu,\sigma) = \frac{1}{2} \left[ 1 + \operatorname{erf}\left( \frac{x-\mu}{\sigma\sqrt{2}} \right) \right]" alt="Cumulative distribution function for a normal distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="center" data-equation="eq:normal_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/normal/cdf/docs/img/equation_normal_cdf.svg" alt="Cumulative distribution function for a normal distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `µ` is the mean and `σ` is the standard deviation.
     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/normal/cdf' );
     50 ```
     51 
     52 #### cdf( x, mu, sigma )
     53 
     54 Evaluates the [cumulative distribution function][cdf] (CDF) for a [normal][normal-distribution] distribution with parameters `mu` (mean) and `sigma` (standard deviation).
     55 
     56 ```javascript
     57 var y = cdf( 2.0, 0.0, 1.0 );
     58 // returns ~0.977
     59 
     60 y = cdf( 0.0, 0.0, 1.0 );
     61 // returns 0.5
     62 
     63 y = cdf( -1.0, 4.0, 2.0 );
     64 // returns ~0.006
     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 `sigma < 0`, the function returns `NaN`.
     81 
     82 ```javascript
     83 var y = cdf( 2.0, 0.0, -1.0 );
     84 // returns NaN
     85 ```
     86 
     87 If provided `sigma = 0`, the function evaluates the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.
     88 
     89 ```javascript
     90 var y = cdf( 2.0, 8.0, 0.0 );
     91 // returns 0.0
     92 
     93 y = cdf( 8.0, 8.0, 0.0 );
     94 // returns 1.0
     95 
     96 y = cdf( 10.0, 8.0, 0.0 );
     97 // returns 1.0
     98 ```
     99 
    100 #### cdf.factory( mu, sigma )
    101 
    102 Returns a function for evaluating the [cumulative distribution function][cdf] of a normal distribution with parameters `mu` and `sigma`.
    103 
    104 ```javascript
    105 var mycdf = cdf.factory( 10.0, 2.0 );
    106 
    107 var y = mycdf( 10.0 );
    108 // returns 0.5
    109 
    110 y = mycdf( 8.0 );
    111 // returns ~0.159
    112 ```
    113 
    114 </section>
    115 
    116 <!-- /.usage -->
    117 
    118 <section class="examples">
    119 
    120 ## Examples
    121 
    122 <!-- eslint no-undef: "error" -->
    123 
    124 ```javascript
    125 var randu = require( '@stdlib/random/base/randu' );
    126 var cdf = require( '@stdlib/stats/base/dists/normal/cdf' );
    127 
    128 var sigma;
    129 var mu;
    130 var x;
    131 var y;
    132 var i;
    133 
    134 for ( i = 0; i < 10; i++ ) {
    135     x = randu() * 10.0;
    136     mu = (randu() * 10.0) - 5.0;
    137     sigma = randu() * 20.0;
    138     y = cdf( x, mu, sigma );
    139     console.log( 'x: %d, µ: %d, σ: %d, F(x;µ,σ): %d', x, mu, sigma, y );
    140 }
    141 ```
    142 
    143 </section>
    144 
    145 <!-- /.examples -->
    146 
    147 <section class="links">
    148 
    149 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    150 
    151 [normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution
    152 
    153 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    154 
    155 </section>
    156 
    157 <!-- /.links -->