time-to-botec

Benchmark sampling in different programming languages
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README.md (3805B)

      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 Cumulative Distribution Function
     22 
     23 > Evaluate the natural logarithm of the [cumulative distribution function][cdf] for an [exponential][exponential-distribution] distribution.
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for an [exponential][exponential-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:exponential_cdf" align="center" raw="F(x;\lambda) = \begin{cases} 1-e^{-\lambda x} & x \ge 0 \\ 0 & x < 0 \end{cases}" alt="Cumulative distribution function for an exponential distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F(x;\lambda) = \begin{cases} 1-e^{-\lambda x} &amp; x \ge 0 \\ 0 &amp; x &lt; 0 \end{cases}" data-equation="eq:exponential_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/exponential/logcdf/docs/img/equation_exponential_cdf.svg" alt="Cumulative distribution function for an 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 logcdf = require( '@stdlib/stats/base/dists/exponential/logcdf' );
     50 ```
     51 
     52 #### logcdf( x, lambda )
     53 
     54 Evaluates the natural logarithm of the [cumulative distribution function][cdf] for an [exponential][exponential-distribution] distribution with rate parameter `lambda`.
     55 
     56 ```javascript
     57 var y = logcdf( 2.0, 0.3 );
     58 // returns ~-0.796
     59 
     60 y = logcdf( 10.0, 0.3 );
     61 // returns ~-0.051
     62 ```
     63 
     64 If provided `NaN` as any argument, the function returns `NaN`.
     65 
     66 ```javascript
     67 var y = logcdf( NaN, 0.0 );
     68 // returns NaN
     69 
     70 y = logcdf( 0.0, NaN );
     71 // returns NaN
     72 ```
     73 
     74 If provided `lambda < 0`, the function returns `NaN`.
     75 
     76 ```javascript
     77 var y = logcdf( 2.0, -1.0 );
     78 // returns NaN
     79 ```
     80 
     81 #### logcdf.factory( lambda )
     82 
     83 Returns a function for evaluating the natural logarithm of the [cumulative distribution function (CDF)][cdf] for an exponential distribution with rate parameter `lambda`.
     84 
     85 ```javascript
     86 var mylogcdf = logcdf.factory( 0.1 );
     87 
     88 var y = mylogcdf( 8.0 );
     89 // returns ~-0.597
     90 
     91 y = mylogcdf( 2.0 );
     92 // returns ~-1.708
     93 
     94 y = mylogcdf( 0.0 );
     95 // returns -Infinity
     96 ```
     97 
     98 </section>
     99 
    100 <!-- /.usage -->
    101 
    102 <section class="notes">
    103 
    104 ## Notes
    105 
    106 -   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.
    107 
    108 </section>
    109 
    110 <!-- /.notes -->
    111 
    112 <section class="examples">
    113 
    114 ## Examples
    115 
    116 <!-- eslint no-undef: "error" -->
    117 
    118 ```javascript
    119 var randu = require( '@stdlib/random/base/randu' );
    120 var logcdf = require( '@stdlib/stats/base/dists/exponential/logcdf' );
    121 
    122 var lambda;
    123 var x;
    124 var y;
    125 var i;
    126 
    127 for ( i = 0; i < 10; i++ ) {
    128     x = randu() * 10.0;
    129     lambda = randu() * 10.0;
    130     y = logcdf( x, lambda );
    131     console.log( 'x: %d, λ: %d, ln(F(x;λ)): %d', x, lambda, y );
    132 }
    133 ```
    134 
    135 </section>
    136 
    137 <!-- /.examples -->
    138 
    139 <section class="links">
    140 
    141 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    142 
    143 [exponential-distribution]: https://en.wikipedia.org/wiki/Exponential_distribution
    144 
    145 </section>
    146 
    147 <!-- /.links -->