time-to-botec

Benchmark sampling in different programming languages
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README.md (3869B)

      1 <!--
      2 
      3 @license Apache-2.0
      4 
      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.
     18 
     19 -->
     20 
     21 # Probability Density Function
     22 
     23 > [F][f-distribution] distribution probability density function (PDF).
     24 
     25 <section class="intro">
     26 
     27 The [probability density function][pdf] (PDF) for a [F][f-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:f_pdf" align="center" raw="f(x; d_1,d_2) = \frac{\sqrt{\frac{(d_1\,x)^{d_1}\,\,d_2^{d_2}} {(d_1\,x+d_2)^{d_1+d_2}}}} {x\,\mathrm{B}\!\left(\frac{d_1}{2},\frac{d_2}{2}\right)}" alt="Probability density function (PDF) for an F distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="f(x; d_1,d_2) = \frac{\sqrt{\frac{(d_1\,x)^{d_1}\,\,d_2^{d_2}} {(d_1\,x+d_2)^{d_1+d_2}}}} {x\,\mathrm{B}\!\left(\frac{d_1}{2},\frac{d_2}{2}\right)}" data-equation="eq:f_pdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/f/pdf/docs/img/equation_f_pdf.svg" alt="Probability density function (PDF) for an F distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `d1` is the numerator degrees of freedom and `d2` is the denominator degrees of freedom and `B` is the `Beta` function.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var pdf = require( '@stdlib/stats/base/dists/f/pdf' );
     50 ```
     51 
     52 #### pdf( x, d1, d2 )
     53 
     54 Evaluates the [probability density function][pdf] (PDF) for a [F][f-distribution] distribution with parameters `d1` (numerator degrees of freedom) and `d2` (denominator degrees of freedom).
     55 
     56 ```javascript
     57 var y = pdf( 2.0, 0.5, 1.0 );
     58 // returns ~0.057
     59 
     60 y = pdf( 0.1, 1.0, 1.0 );
     61 // returns ~0.915
     62 
     63 y = pdf( -1.0, 4.0, 2.0 );
     64 // returns 0.0
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = pdf( NaN, 1.0, 1.0 );
     71 // returns NaN
     72 
     73 y = pdf( 0.0, NaN, 1.0 );
     74 // returns NaN
     75 
     76 y = pdf( 0.0, 1.0, NaN );
     77 // returns NaN
     78 ```
     79 
     80 If provided `d1 <= 0`, the function returns `NaN`.
     81 
     82 ```javascript
     83 var y = pdf( 2.0, 0.0, 1.0 );
     84 // returns NaN
     85 
     86 y = pdf( 2.0, -1.0, 1.0 );
     87 // returns NaN
     88 ```
     89 
     90 If provided `d2 <= 0`, the function returns `NaN`.
     91 
     92 ```javascript
     93 var y = pdf( 2.0, 1.0, 0.0 );
     94 // returns NaN
     95 
     96 y = pdf( 2.0, 1.0, -1.0 );
     97 // returns NaN
     98 ```
     99 
    100 #### pdf.factory( d1, d2 )
    101 
    102 Returns a `function` for evaluating the [PDF][pdf] of a [F][f-distribution] distribution with parameters `d1` (numerator degrees of freedom) and `d2` (denominator degrees of freedom).
    103 
    104 ```javascript
    105 var mypdf = pdf.factory( 6.0, 7.0 );
    106 var y = mypdf( 7.0 );
    107 // returns ~0.004
    108 
    109 y = mypdf( 2.0 );
    110 // returns ~0.166
    111 ```
    112 
    113 </section>
    114 
    115 <!-- /.usage -->
    116 
    117 <section class="examples">
    118 
    119 ## Examples
    120 
    121 <!-- eslint no-undef: "error" -->
    122 
    123 ```javascript
    124 var randu = require( '@stdlib/random/base/randu' );
    125 var pdf = require( '@stdlib/stats/base/dists/f/pdf' );
    126 
    127 var d1;
    128 var d2;
    129 var x;
    130 var y;
    131 var i;
    132 
    133 for ( i = 0; i < 10; i++ ) {
    134     x = randu() * 4.0;
    135     d1 = randu() * 10.0;
    136     d2 = randu() * 10.0;
    137     y = pdf( x, d1, d2 );
    138     console.log( 'x: %d, d1: %d, d2: %d, f(x;d1,d2): %d', x.toFixed( 4 ), d1.toFixed( 4 ), d2.toFixed( 4 ), y.toFixed( 4 ) );
    139 }
    140 ```
    141 
    142 </section>
    143 
    144 <!-- /.examples -->
    145 
    146 <section class="links">
    147 
    148 [f-distribution]: https://en.wikipedia.org/wiki/F_distribution
    149 
    150 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function
    151 
    152 </section>
    153 
    154 <!-- /.links -->