time-to-botec

Benchmark sampling in different programming languages
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README.md (4055B)

      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 Cumulative Distribution Function
     22 
     23 > [Laplace][laplace-distribution] distribution logarithm of [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for a [Laplace][laplace-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:laplace_cdf" align="center" raw="F(x;\mu,b) =\tfrac{1}{2} + \tfrac{1}{2} \operatorname{sgn}(x-\mu) \left(1-\exp \left(-\frac{|x-\mu|}{b} \right ) \right )" alt="Cumulative distribution function for a Laplace distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F(x;\mu,b) =\tfrac{1}{2} + \tfrac{1}{2} \operatorname{sgn}(x-\mu) \left(1-\exp \left(-\frac{|x-\mu|}{b} \right ) \right )" data-equation="eq:laplace_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/laplace/logcdf/docs/img/equation_laplace_cdf.svg" alt="Cumulative distribution function 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.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var logcdf = require( '@stdlib/stats/base/dists/laplace/logcdf' );
     50 ```
     51 
     52 #### logcdf( x, mu, b )
     53 
     54 Evaluates the logarithm of the [cumulative distribution function][cdf] (CDF) for a [Laplace][laplace-distribution] distribution with parameters `mu` (location parameter) and `b > 0` (scale parameter).
     55 
     56 ```javascript
     57 var y = logcdf( 2.0, 0.0, 1.0 );
     58 // returns ~-0.07
     59 
     60 y = logcdf( 5.0, 10.0, 3.0 );
     61 // returns ~-2.36
     62 ```
     63 
     64 If provided `NaN` as any argument, the function returns `NaN`.
     65 
     66 ```javascript
     67 var y = logcdf( NaN, 0.0, 1.0 );
     68 // returns NaN
     69 
     70 y = logcdf( 0.0, NaN, 1.0 );
     71 // returns NaN
     72 
     73 y = logcdf( 0.0, 0.0, NaN );
     74 // returns NaN
     75 ```
     76 
     77 If provided `b <= 0`, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = logcdf( 2.0, 0.0, -1.0 );
     81 // returns NaN
     82 
     83 y = logcdf( 2.0, 0.0, 0.0 );
     84 // returns NaN
     85 ```
     86 
     87 #### logcdf.factory( mu, b )
     88 
     89 Returns a function for evaluating the logarithm of the [cumulative distribution function][cdf] of a [Laplace][laplace-distribution] distribution with parameters `mu` (location parameter) and `b > 0` (scale parameter).
     90 
     91 ```javascript
     92 var mylogcdf = logcdf.factory( 3.0, 1.5 );
     93 
     94 var y = mylogcdf( 1.0 );
     95 // returns ~-2.026
     96 
     97 y = mylogcdf( 4.0 );
     98 // returns ~-0.297
     99 ```
    100 
    101 </section>
    102 
    103 <!-- /.usage -->
    104 
    105 <section class="notes">
    106 
    107 ## Notes
    108 
    109 -   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.
    110 
    111 </section>
    112 
    113 <!-- /.notes -->
    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 logcdf = require( '@stdlib/stats/base/dists/laplace/logcdf' );
    124 
    125 var mu;
    126 var b;
    127 var x;
    128 var y;
    129 var i;
    130 
    131 for ( i = 0; i < 100; i++ ) {
    132     x = randu() * 10.0;
    133     mu = randu() * 10.0;
    134     b = randu() * 10.0;
    135     y = logcdf( x, mu, b );
    136     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 ) );
    137 }
    138 ```
    139 
    140 </section>
    141 
    142 <!-- /.examples -->
    143 
    144 <section class="links">
    145 
    146 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    147 
    148 [laplace-distribution]: https://en.wikipedia.org/wiki/Laplace_distribution
    149 
    150 </section>
    151 
    152 <!-- /.links -->