time-to-botec

Benchmark sampling in different programming languages
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README.md (4041B)

      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 > [Gamma][gamma-distribution] distribution probability density function (PDF).
     24 
     25 <section class="intro">
     26 
     27 The [probability density function][pdf] (PDF) for a [gamma][gamma-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:gamma_pdf" align="center" raw="f(x;\alpha,\beta)=\frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha \,-\, 1} e^{- \beta x }" alt="Probability density function (PDF) for a Gamma distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="f(x;\alpha,\beta)=\frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha \,-\, 1} e^{- \beta x }" data-equation="eq:gamma_pdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/gamma/pdf/docs/img/equation_gamma_pdf.svg" alt="Probability density function (PDF) for a Gamma distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `α > 0` is the shape parameter and `β > 0` is the rate parameter.
     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/gamma/pdf' );
     50 ```
     51 
     52 #### pdf( x, alpha, beta )
     53 
     54 Evaluates the [probability density function][pdf] (PDF) for a [gamma][gamma-distribution]  distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).
     55 
     56 ```javascript
     57 var y = pdf( 2.0, 0.5, 1.0 );
     58 // returns ~0.054
     59 
     60 y = pdf( 0.1, 1.0, 1.0 );
     61 // returns ~0.905
     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 `alpha < 0`, the function returns `NaN`.
     81 
     82 ```javascript
     83 var y = pdf( 2.0, -0.5, 1.0 );
     84 // returns NaN
     85 ```
     86 
     87 If provided `alpha = 0`, the function evaluates the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `0`.
     88 
     89 ```javascript
     90 var y = pdf( 2.0, 0.0, 2.0 );
     91 // returns 0.0
     92 
     93 y = pdf( 0.0, 0.0, 2.0 );
     94 // returns Infinity
     95 ```
     96 
     97 If provided `beta <= 0`, the function returns `NaN`.
     98 
     99 ```javascript
    100 var y = pdf( 2.0, 1.0, 0.0 );
    101 // returns NaN
    102 
    103 y = pdf( 2.0, 1.0, -1.0 );
    104 // returns NaN
    105 ```
    106 
    107 #### pdf.factory( alpha, beta )
    108 
    109 Returns a `function` for evaluating the [PDF][pdf] of a [gamma][gamma-distribution] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).
    110 
    111 ```javascript
    112 var mypdf = pdf.factory( 3.0, 1.5 );
    113 
    114 var y = mypdf( 1.0 );
    115 // returns ~0.377
    116 
    117 y = mypdf( 4.0 );
    118 // returns ~0.067
    119 ```
    120 
    121 </section>
    122 
    123 <!-- /.usage -->
    124 
    125 <section class="examples">
    126 
    127 ## Examples
    128 
    129 <!-- eslint no-undef: "error" -->
    130 
    131 ```javascript
    132 var randu = require( '@stdlib/random/base/randu' );
    133 var pdf = require( '@stdlib/stats/base/dists/gamma/pdf' );
    134 
    135 var alpha;
    136 var beta;
    137 var x;
    138 var y;
    139 var i;
    140 
    141 for ( i = 0; i < 10; i++ ) {
    142     x = randu() * 3.0;
    143     alpha = randu() * 5.0;
    144     beta = randu() * 5.0;
    145     y = pdf( x, alpha, beta );
    146     console.log( 'x: %d, α: %d, β: %d, f(x;α,β): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
    147 }
    148 ```
    149 
    150 </section>
    151 
    152 <!-- /.examples -->
    153 
    154 <section class="links">
    155 
    156 [gamma-distribution]: https://en.wikipedia.org/wiki/Gamma_distribution
    157 
    158 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function
    159 
    160 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    161 
    162 </section>
    163 
    164 <!-- /.links -->