time-to-botec

Benchmark sampling in different programming languages
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README.md (3993B)

      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.
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     19 -->
     20 
     21 # Logarithm of Cumulative Distribution Function
     22 
     23 > [Gumbel][gumbel-distribution] distribution logarithm of [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for a [Gumbel][gumbel-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:gumbel_cdf" align="center" raw="F\left( x; \mu, \beta \right ) = e^{{-e^{{-(x-\mu )/\beta }}}}" alt="Cumulative distribution function for a Gumbel distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F\left( x; \mu, \beta \right ) = e^{{-e^{{-(x-\mu )/\beta }}}}" data-equation="eq:gumbel_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/gumbel/logcdf/docs/img/equation_gumbel_cdf.svg" alt="Cumulative distribution function for a Gumbel distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `mu` is the location parameter and `beta > 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/gumbel/logcdf' );
     50 ```
     51 
     52 #### logcdf( x, mu, beta )
     53 
     54 Evaluates the logarithm of the [cumulative distribution function][cdf] (CDF) for a [Gumbel][gumbel-distribution] distribution with parameters `mu` (location parameter) and `beta` (scale parameter).
     55 
     56 ```javascript
     57 var y = logcdf( 10.0, 0.0, 3.0 );
     58 // returns ~-0.036
     59 
     60 y = logcdf( -2.0, 0.0, 3.0 );
     61 // returns ~-1.948
     62 
     63 y = logcdf( 0.0, 0.0, 1.0 );
     64 // returns ~-1
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = logcdf( NaN, 0.0, 1.0 );
     71 // returns NaN
     72 
     73 y = logcdf( 0.0, NaN, 1.0 );
     74 // returns NaN
     75 
     76 y = logcdf( 0.0, 0.0, NaN );
     77 // returns NaN
     78 ```
     79 
     80 If provided `beta <= 0`, the function returns `NaN`.
     81 
     82 ```javascript
     83 var y = logcdf( 2.0, 0.0, -1.0 );
     84 // returns NaN
     85 
     86 y = logcdf( 2.0, 0.0, 0.0 );
     87 // returns NaN
     88 ```
     89 
     90 #### logcdf.factory( mu, beta )
     91 
     92 Returns a function for evaluating the logarithm of the [cumulative distribution function][cdf] of a [Gumbel][gumbel-distribution] distribution with parameters `mu` (location parameter) and `beta` (scale parameter).
     93 
     94 ```javascript
     95 var mylogcdf = logcdf.factory( 0.0, 3.0 );
     96 
     97 var y = mylogcdf( 10.0 );
     98 // returns ~-0.036
     99 
    100 y = mylogcdf( -2.0 );
    101 // returns ~-1.948
    102 ```
    103 
    104 </section>
    105 
    106 <!-- /.usage -->
    107 
    108 <section class="notes">
    109 
    110 ## Notes
    111 
    112 -   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.
    113 
    114 </section>
    115 
    116 <!-- /.notes -->
    117 
    118 <section class="examples">
    119 
    120 ## Examples
    121 
    122 <!-- eslint no-undef: "error" -->
    123 
    124 ```javascript
    125 var randu = require( '@stdlib/random/base/randu' );
    126 var logcdf = require( '@stdlib/stats/base/dists/gumbel/logcdf' );
    127 
    128 var beta;
    129 var mu;
    130 var x;
    131 var y;
    132 var i;
    133 
    134 for ( i = 0; i < 100; i++ ) {
    135     x = randu() * 10.0;
    136     mu = randu() * 10.0;
    137     beta = randu() * 10.0;
    138     y = logcdf( x, mu, beta );
    139     console.log( 'x: %d, µ: %d, β: %d, ln(F(x;µ,β)): %d', x.toFixed( 4 ), mu.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
    140 }
    141 ```
    142 
    143 </section>
    144 
    145 <!-- /.examples -->
    146 
    147 <section class="links">
    148 
    149 [gumbel-distribution]: https://en.wikipedia.org/wiki/Gumbel_distribution
    150 
    151 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    152 
    153 </section>
    154 
    155 <!-- /.links -->