time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

README.md (4051B)

      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
     10 
     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 # Logarithm of Probability Density Function
     22 
     23 > Evaluate the natural logarithm of the probability density function (PDF) for an [inverse gamma][inverse-gamma] distribution.
     24 
     25 <section class="intro">
     26 
     27 The [probability density function][pdf] (PDF) for an [inverse gamma][inverse-gamma] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:invgamma_pdf" align="center" raw="{\displaystyle f(x;\alpha ,\beta )={\frac {\beta ^{\alpha }}{\Gamma (\alpha )}}x^{-\alpha -1}\exp \left(-{\frac {\beta }{x}}\right)}" alt="Probability density function (PDF) for an inverse gamma distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="{\displaystyle f(x;\alpha ,\beta )={\frac {\beta ^{\alpha }}{\Gamma (\alpha )}}x^{-\alpha -1}\exp \left(-{\frac {\beta }{x}}\right)}" data-equation="eq:invgamma_pdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/invgamma/logpdf/docs/img/equation_invgamma_pdf.svg" alt="Probability density function (PDF) for an inverse gamma distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `alpha > 0` is the shape parameter and `beta > 0` is the scale parameter.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var logpdf = require( '@stdlib/stats/base/dists/invgamma/logpdf' );
     50 ```
     51 
     52 #### logpdf( x, alpha, beta )
     53 
     54 Evaluates the natural logarithm of the [probability density function][pdf] (PDF) for an [inverse gamma][inverse-gamma] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).
     55 
     56 ```javascript
     57 var y = logpdf( 2.0, 0.5, 1.0 );
     58 // returns ~-2.112
     59 
     60 y = logpdf( 0.2, 1.0, 1.0 );
     61 // returns ~-1.781
     62 
     63 y = logpdf( -1.0, 4.0, 2.0 );
     64 // returns -Infinity
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = logpdf( NaN, 1.0, 1.0 );
     71 // returns NaN
     72 
     73 y = logpdf( 0.0, NaN, 1.0 );
     74 // returns NaN
     75 
     76 y = logpdf( 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 = logpdf( 2.0, 0.0, 1.0 );
     84 // returns NaN
     85 
     86 y = logpdf( 2.0, -0.5, 1.0 );
     87 // returns NaN
     88 ```
     89 
     90 If provided `beta <= 0`, the function returns `NaN`.
     91 
     92 ```javascript
     93 var y = logpdf( 2.0, 1.0, 0.0 );
     94 // returns NaN
     95 
     96 y = logpdf( 2.0, 1.0, -1.0 );
     97 // returns NaN
     98 ```
     99 
    100 #### logpdf.factory( alpha, beta )
    101 
    102 Returns a `function` for evaluating the natural logarithm of the [PDF][pdf] for an [inverse gamma][inverse-gamma] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).
    103 
    104 ```javascript
    105 var mylogPDF = logpdf.factory( 6.0, 7.0 );
    106 
    107 var y = mylogPDF( 2.0 );
    108 // returns ~-1.464
    109 ```
    110 
    111 </section>
    112 
    113 <!-- /.usage -->
    114 
    115 <section class="examples">
    116 
    117 ## Examples
    118 
    119 <!-- eslint no-undef: "error" -->
    120 
    121 ```javascript
    122 var randu = require( '@stdlib/random/base/randu' );
    123 var logpdf = require( '@stdlib/stats/base/dists/invgamma/logpdf' );
    124 
    125 var alpha;
    126 var beta;
    127 var x;
    128 var y;
    129 var i;
    130 
    131 for ( i = 0; i < 10; i++ ) {
    132     x = randu() * 2.0;
    133     alpha = randu() * 5.0;
    134     beta = randu() * 5.0;
    135     y = logpdf( x, alpha, beta );
    136     console.log( 'x: %d, α: %d, β: %d, ln(f(x;α,β)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
    137 }
    138 ```
    139 
    140 </section>
    141 
    142 <!-- /.examples -->
    143 
    144 <section class="links">
    145 
    146 [inverse-gamma]: https://en.wikipedia.org/wiki/Inverse-gamma_distribution
    147 
    148 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function
    149 
    150 </section>
    151 
    152 <!-- /.links -->