time-to-botec

Benchmark sampling in different programming languages
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README.md (4241B)

      1 <!--
      2 
      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
     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.
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     19 -->
     20 
     21 # Logarithm of Probability Density Function
     22 
     23 > [Logistic][logistic-distribution] distribution logarithm of [probability density function (PDF)][pdf].
     24 
     25 <section class="intro">
     26 
     27 The [probability density function][pdf] (PDF) for a [logistic][logistic-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:logistic_pdf" align="center" raw="f(x; \mu,s) = \frac{e^{-\frac{x-\mu}{s}}} {s\left(1+e^{-\frac{x-\mu}{s}}\right)^2}" alt="Probability density function (PDF) for a logistic distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="f(x; \mu,s) = \frac{e^{-\frac{x-\mu}{s}}} {s\left(1+e^{-\frac{x-\mu}{s}}\right)^2}" data-equation="eq:logistic_pdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/logistic/logpdf/docs/img/equation_logistic_pdf.svg" alt="Probability density function (PDF) for a logistic distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `mu` is the location parameter and `s` 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/logistic/logpdf' );
     50 ```
     51 
     52 #### logpdf( x, mu, s )
     53 
     54 Evaluates the logarithm of the [probability density function][pdf] (PDF) for a [logistic][logistic-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter).
     55 
     56 ```javascript
     57 var y = logpdf( 2.0, 0.0, 1.0 );
     58 // returns ~-2.254
     59 
     60 y = logpdf( -1.0, 4.0, 4.0 );
     61 // returns ~-3.14
     62 ```
     63 
     64 If provided `NaN` as any argument, the function returns `NaN`.
     65 
     66 ```javascript
     67 var y = logpdf( NaN, 0.0, 1.0 );
     68 // returns NaN
     69 
     70 y = logpdf( 0.0, NaN, 1.0 );
     71 // returns NaN
     72 
     73 y = logpdf( 0.0, 0.0, NaN );
     74 // returns NaN
     75 ```
     76 
     77 If provided `s < 0`, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = logpdf( 2.0, 0.0, -1.0 );
     81 // returns NaN
     82 ```
     83 
     84 If provided `s = 0`, the function evaluates the logarithm of the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.
     85 
     86 ```javascript
     87 var y = logpdf( 2.0, 8.0, 0.0 );
     88 // returns -Infinity
     89 
     90 y = logpdf( 8.0, 8.0, 0.0 );
     91 // returns Infinity
     92 ```
     93 
     94 #### logpdf.factory( mu, s )
     95 
     96 Returns a function for evaluating the logarithm of the [probability density function][pdf] (PDF) of a [logistic][logistic-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter).
     97 
     98 ```javascript
     99 var mylogpdf = logpdf.factory( 10.0, 2.0 );
    100 
    101 var y = mylogpdf( 10.0 );
    102 // returns ~-2.079
    103 
    104 y = mylogpdf( 5.0 );
    105 // returns ~-3.351
    106 ```
    107 
    108 </section>
    109 
    110 <!-- /.usage -->
    111 
    112 <section class="notes">
    113 
    114 ## Notes
    115 
    116 -   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.
    117 
    118 </section>
    119 
    120 <!-- /.notes -->
    121 
    122 <section class="examples">
    123 
    124 ## Examples
    125 
    126 <!-- eslint no-undef: "error" -->
    127 
    128 ```javascript
    129 var randu = require( '@stdlib/random/base/randu' );
    130 var logpdf = require( '@stdlib/stats/base/dists/logistic/logpdf' );
    131 
    132 var mu;
    133 var s;
    134 var x;
    135 var y;
    136 var i;
    137 
    138 for ( i = 0; i < 10; i++ ) {
    139     x = randu() * 10.0;
    140     mu = randu() * 10.0;
    141     s = randu() * 10.0;
    142     y = logpdf( x, mu, s );
    143     console.log( 'x: %d, µ: %d, s: %d, ln(f(x;µ,s)): %d', x, mu, s, y );
    144 }
    145 ```
    146 
    147 </section>
    148 
    149 <!-- /.examples -->
    150 
    151 <section class="links">
    152 
    153 [logistic-distribution]: https://en.wikipedia.org/wiki/Logistic_distribution
    154 
    155 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function
    156 
    157 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    158 
    159 </section>
    160 
    161 <!-- /.links -->