time-to-botec

Benchmark sampling in different programming languages
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README.md (4123B)

      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
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     19 -->
     20 
     21 # Logarithm of Probability Density Function
     22 
     23 > Evaluate the natural logarithm of the probability density function (PDF) for a [lognormal][lognormal-distribution] distribution.
     24 
     25 <section class="intro">
     26 
     27 The [probability density function][pdf] (PDF) for a [lognormal][lognormal-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:pdf" align="center" raw="f(x;\mu,\sigma) = \frac{1}{x\sqrt{2\pi\sigma^2}} e^{-\frac{\left(\ln x-\mu\right)^2}{2\sigma^2}}" alt="Probability density function (PDF) for a lognormal distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="f(x;\mu,\sigma) = \frac{1}{x\sqrt{2\pi\sigma^2}} e^{-\frac{\left(\ln x-\mu\right)^2}{2\sigma^2}}" data-equation="eq:pdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/lognormal/logpdf/docs/img/equation_pdf.svg" alt="Probability density function (PDF) for a lognormal distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `mu` is the location parameter and `sigma > 0` is the scale parameter. According to the definition, the _natural logarithm_ of a random variable from a
     39 [lognormal distribution][lognormal-distribution] follows a [normal distribution][normal-distribution].
     40 
     41 </section>
     42 
     43 <!-- /.intro -->
     44 
     45 <section class="usage">
     46 
     47 ## Usage
     48 
     49 ```javascript
     50 var logpdf = require( '@stdlib/stats/base/dists/lognormal/logpdf' );
     51 ```
     52 
     53 #### logpdf( x, mu, sigma )
     54 
     55 Evaluates the natural logarithm of the [probability density function][pdf] (PDF) for a [lognormal][lognormal-distribution] distribution with parameters `mu` (location parameter) and `sigma` (scale parameter).
     56 
     57 ```javascript
     58 var y = logpdf( 2.0, 0.0, 1.0 );
     59 // returns ~-1.852
     60 
     61 y = logpdf( 1.0, 0.0, 1.0 );
     62 // returns ~-0.919
     63 
     64 y = logpdf( 1.0, 3.0, 1.0 );
     65 // returns ~-5.419
     66 ```
     67 
     68 If provided `NaN` as any argument, the function returns `NaN`.
     69 
     70 ```javascript
     71 var y = logpdf( NaN, 0.0, 1.0 );
     72 // returns NaN
     73 
     74 y = logpdf( 0.0, NaN, 1.0 );
     75 // returns NaN
     76 
     77 y = logpdf( 0.0, 0.0, NaN );
     78 // returns NaN
     79 ```
     80 
     81 If provided `sigma <= 0`, the function returns `NaN`.
     82 
     83 ```javascript
     84 var y = logpdf( 2.0, 0.0, -1.0 );
     85 // returns NaN
     86 
     87 y = logpdf( 2.0, 0.0, 0.0 );
     88 // returns NaN
     89 ```
     90 
     91 #### logpdf.factory( mu, sigma )
     92 
     93 Returns a function for evaluating the natural logarithm of the [probability density function][pdf] (PDF) of a [lognormal][lognormal-distribution] distribution with parameters `mu` (location parameter) and `sigma` (scale parameter).
     94 
     95 ```javascript
     96 var mylogpdf = logpdf.factory( 4.0, 2.0 );
     97 var y = mylogpdf( 10.0 );
     98 // returns ~-4.275
     99 
    100 y = mylogpdf( 2.0 );
    101 // returns ~-3.672
    102 ```
    103 
    104 </section>
    105 
    106 <!-- /.usage -->
    107 
    108 <section class="examples">
    109 
    110 ## Examples
    111 
    112 <!-- eslint no-undef: "error" -->
    113 
    114 ```javascript
    115 var randu = require( '@stdlib/random/base/randu' );
    116 var logpdf = require( '@stdlib/stats/base/dists/lognormal/logpdf' );
    117 
    118 var sigma;
    119 var mu;
    120 var x;
    121 var y;
    122 var i;
    123 
    124 for ( i = 0; i < 10; i++ ) {
    125     x = randu() * 10.0;
    126     mu = (randu() * 10.0) - 5.0;
    127     sigma = randu() * 20.0;
    128     y = logpdf( x, mu, sigma );
    129     console.log( 'x: %d, µ: %d, σ: %d, ln(f(x;µ,σ)): %d', x.toFixed( 4 ), mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
    130 }
    131 ```
    132 
    133 </section>
    134 
    135 <!-- /.examples -->
    136 
    137 <section class="links">
    138 
    139 [lognormal-distribution]: https://en.wikipedia.org/wiki/Lognormal_distribution
    140 
    141 [normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution
    142 
    143 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function
    144 
    145 </section>
    146 
    147 <!-- /.links -->