time-to-botec

Benchmark sampling in different programming languages
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README.md (3722B)

      1 <!--
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      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
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     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 # Probability Density Function
     22 
     23 > [Arcsine][arcsine-distribution] distribution [probability density function][pdf] (PDF).
     24 
     25 <section class="intro">
     26 
     27 The [probability density function][pdf] (PDF) for an [arcsine][arcsine-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:arcsine_pdf" align="center" raw="f(x;a,b)=\begin{cases} {\frac{1}{\pi {\sqrt{(x-a)(b-x)}}}} & \text{for } x \in [a,b] \\ 0 & \text{otherwise} \end{cases}" alt="Probability density function (PDF) for an arcsine distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="f(x;a,b)=\begin{cases} {\frac{1}{\pi {\sqrt{(x-a)(b-x)}}}} &amp; \text{for } x \in [a,b] \\ 0 &amp; \text{otherwise} \end{cases}" data-equation="eq:arcsine_pdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/pdf/docs/img/equation_arcsine_pdf.svg" alt="Probability density function (PDF) for an arcsine distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `a` is the minimum support and `b` is the maximum support of the distribution. The parameters must satisfy `a < b`.
     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/arcsine/pdf' );
     50 ```
     51 
     52 #### pdf( x, a, b )
     53 
     54 Evaluates the [probability density function][pdf] (PDF) for an [arcsine][arcsine-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
     55 
     56 ```javascript
     57 var y = pdf( 2.0, 0.0, 4.0 );
     58 // returns ~0.159
     59 
     60 y = pdf( 5.0, 0.0, 4.0 );
     61 // returns 0.0
     62 
     63 y = pdf( 0.25, 0.0, 1.0 );
     64 // returns ~0.735
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = pdf( NaN, 0.0, 1.0 );
     71 // returns NaN
     72 
     73 y = pdf( 0.0, NaN, 1.0 );
     74 // returns NaN
     75 
     76 y = pdf( 0.0, 0.0, NaN );
     77 // returns NaN
     78 ```
     79 
     80 If provided `a >= b`, the function returns `NaN`.
     81 
     82 ```javascript
     83 var y = pdf( 2.5, 3.0, 2.0 );
     84 // returns NaN
     85 
     86 y = pdf( 2.5, 3.0, 3.0 );
     87 // returns NaN
     88 ```
     89 
     90 #### pdf.factory( a, b )
     91 
     92 Returns a `function` for evaluating the [PDF][pdf] of an [arcsine][arcsine-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
     93 
     94 ```javascript
     95 var myPDF = pdf.factory( 6.0, 7.0 );
     96 var y = myPDF( 7.0 );
     97 // returns Infinity
     98 
     99 y = myPDF( 5.0 );
    100 // returns 0.0
    101 ```
    102 
    103 </section>
    104 
    105 <!-- /.usage -->
    106 
    107 <section class="examples">
    108 
    109 ## Examples
    110 
    111 <!-- eslint no-undef: "error" -->
    112 
    113 ```javascript
    114 var randu = require( '@stdlib/random/base/randu' );
    115 var pdf = require( '@stdlib/stats/base/dists/arcsine/pdf' );
    116 
    117 var a;
    118 var b;
    119 var x;
    120 var y;
    121 var i;
    122 
    123 for ( i = 0; i < 25; i++ ) {
    124     x = ( randu()*20.0 )- 10.0;
    125     a = ( randu()*20.0 )- 20.0;
    126     b = a + ( randu()*40.0 );
    127     y = pdf( x, a, b );
    128     console.log( 'x: %d, a: %d, b: %d, f(x;a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
    129 }
    130 ```
    131 
    132 </section>
    133 
    134 <!-- /.examples -->
    135 
    136 <section class="links">
    137 
    138 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function
    139 
    140 [arcsine-distribution]: https://en.wikipedia.org/wiki/Arcsine_distribution
    141 
    142 </section>
    143 
    144 <!-- /.links -->