time-to-botec

Benchmark sampling in different programming languages
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README.md (3760B)

      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 # Logarithm of Probability Density Function
     22 
     23 > Evaluate the natural logarithm of the probability density function (PDF) for an [exponential][exponential-distribution] distribution.
     24 
     25 <section class="intro">
     26 
     27 The [probability density function][pdf] (PDF) for an [exponential][exponential-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:exponential_pdf" align="center" raw="f(x;\lambda) = \begin{cases} \lambda e^{-\lambda x} & x \ge 0 \\ 0 & x < 0 \end{cases}" alt="Probability density function (PDF) for a Exponential distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="f(x;\lambda) = \begin{cases} \lambda e^{-\lambda x} &amp; x \ge 0 \\ 0 &amp; x &lt; 0 \end{cases}" data-equation="eq:exponential_pdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/exponential/logpdf/docs/img/equation_exponential_pdf.svg" alt="Probability density function (PDF) for a Exponential distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `λ` is the rate 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/exponential/logpdf' );
     50 ```
     51 
     52 #### logpdf( x, lambda )
     53 
     54 Evaluates the natural logarithm of the [probability density function][pdf] (PDF) for an [exponential][exponential-distribution] distribution with rate parameter `lambda`.
     55 
     56 ```javascript
     57 var y = logpdf( 2.0, 0.3 );
     58 // returns ~-1.804
     59 
     60 y = logpdf( 2.0, 1.0 );
     61 // returns ~-2.0
     62 ```
     63 
     64 If provided `NaN` as any argument, the function returns `NaN`.
     65 
     66 ```javascript
     67 var y = logpdf( NaN, 0.0 );
     68 // returns NaN
     69 
     70 y = logpdf( 0.0, NaN );
     71 // returns NaN
     72 ```
     73 
     74 If provided `lambda < 0`, the function returns `NaN`.
     75 
     76 ```javascript
     77 var y = logpdf( 2.0, -1.0 );
     78 // returns NaN
     79 ```
     80 
     81 #### logpdf.factory( lambda )
     82 
     83 Returns a function for evaluating the natural logarithm of the probability density function ([PDF][pdf]) for an exponential distribution with rate parameter `lambda`.
     84 
     85 ```javascript
     86 var mylogpdf = logpdf.factory( 0.1 );
     87 
     88 var y = mylogpdf( 8.0 );
     89 // returns ~-3.103
     90 
     91 y = mylogpdf( 5.0 );
     92 // returns ~-2.803
     93 ```
     94 
     95 </section>
     96 
     97 <!-- /.usage -->
     98 
     99 <section class="notes">
    100 
    101 ## Notes
    102 
    103 -   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.
    104 
    105 </section>
    106 
    107 <!-- /.notes -->
    108 
    109 <section class="examples">
    110 
    111 ## Examples
    112 
    113 <!-- eslint no-undef: "error" -->
    114 
    115 ```javascript
    116 var randu = require( '@stdlib/random/base/randu' );
    117 var logpdf = require( '@stdlib/stats/base/dists/exponential/logpdf' );
    118 
    119 var lambda;
    120 var x;
    121 var y;
    122 var i;
    123 
    124 for ( i = 0; i < 10; i++ ) {
    125     x = randu() * 10.0;
    126     lambda = randu() * 10.0;
    127     y = logpdf( x, lambda );
    128     console.log( 'x: %d, λ: %d, ln(f(x;λ)): %d', x, lambda, y );
    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 [exponential-distribution]: https://en.wikipedia.org/wiki/Exponential_distribution
    141 
    142 </section>
    143 
    144 <!-- /.links -->