time-to-botec

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

README.md (4028B)

      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 > [Laplace][laplace-distribution] distribution logarithm of probability density function (PDF).
     24 
     25 <section class="intro">
     26 
     27 The [probability density function][pdf] (PDF) for a [Laplace][laplace-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:laplace_pdf" align="center" raw="f(x\mid\mu,b) = \frac{1}{2b} \exp \left( -\frac{|x-\mu|}{b} \right)" alt="Probability density function (PDF) for a Laplace distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="f(x\mid\mu,b) = \frac{1}{2b} \exp \left( -\frac{|x-\mu|}{b} \right)" data-equation="eq:laplace_pdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/laplace/logpdf/docs/img/equation_laplace_pdf.svg" alt="Probability density function (PDF) for a Laplace distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `mu` is the location parameter and `b > 0` is the scale parameter (also called diversity).
     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/laplace/logpdf' );
     50 ```
     51 
     52 #### logpdf( x, mu, b )
     53 
     54 Evaluates the logarithm of the [probability density function][pdf] (PDF) for a [Laplace][laplace-distribution] distribution with parameters `mu` (location parameter) and `b > 0` (scale parameter).
     55 
     56 ```javascript
     57 var y = logpdf( 2.0, 0.0, 1.0 );
     58 // returns ~-2.693
     59 
     60 y = logpdf( -1.0, 2.0, 3.0 );
     61 // returns ~-2.792
     62 
     63 y = logpdf( 2.5, 2.0, 3.0 );
     64 // returns ~-1.958
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = logpdf( NaN, 0.0, 1.0 );
     71 // returns NaN
     72 
     73 y = logpdf( 0.0, NaN, 1.0 );
     74 // returns NaN
     75 
     76 y = logpdf( 0.0, 0.0, NaN );
     77 // returns NaN
     78 ```
     79 
     80 If provided `b <= 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, 8.0, 0.0 );
     87 // returns NaN
     88 ```
     89 
     90 #### logpdf.factory( mu, b )
     91 
     92 Return a `function` for evaluating the logarithm of the [PDF][pdf] for a [Laplace][laplace-distribution] distribution with parameters `mu` (location parameter) and `b > 0` (scale parameter).
     93 
     94 ```javascript
     95 var mylogpdf = logpdf.factory( 10.0, 2.0 );
     96 
     97 var y = mylogpdf( 10.0 );
     98 // returns ~-1.386
     99 
    100 y = mylogpdf( 5.0 );
    101 // returns ~-3.886
    102 
    103 y = mylogpdf( 12.0 );
    104 // returns ~-2.386
    105 ```
    106 
    107 </section>
    108 
    109 <!-- /.usage -->
    110 
    111 <section class="notes">
    112 
    113 ## Notes
    114 
    115 -   In virtually all cases, using the `logpdf` or `logcdf` functions is preferable to manually computing the logarithm of the `pdf` or `cdf`, respectively, since the latter is prone to overflow and underflow.
    116 
    117 </section>
    118 
    119 <!-- /.notes -->
    120 
    121 <section class="examples">
    122 
    123 ## Examples
    124 
    125 <!-- eslint no-undef: "error" -->
    126 
    127 ```javascript
    128 var randu = require( '@stdlib/random/base/randu' );
    129 var logpdf = require( '@stdlib/stats/base/dists/laplace/logpdf' );
    130 
    131 var mu;
    132 var b;
    133 var x;
    134 var y;
    135 var i;
    136 
    137 for ( i = 0; i < 100; i++ ) {
    138     x = randu() * 10.0;
    139     mu = randu() * 10.0;
    140     b = randu() * 10.0;
    141     y = logpdf( x, mu, b );
    142     console.log( 'x: %d, µ: %d, b: %d, ln(f(x;µ,b)): %d', x.toFixed( 4 ), mu.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
    143 }
    144 ```
    145 
    146 </section>
    147 
    148 <!-- /.examples -->
    149 
    150 <section class="links">
    151 
    152 [laplace-distribution]: https://en.wikipedia.org/wiki/Laplace_distribution
    153 
    154 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function
    155 
    156 </section>
    157 
    158 <!-- /.links -->