time-to-botec

Benchmark sampling in different programming languages
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README.md (4361B)

      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
     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 > Evaluate the natural logarithm of the [cumulative distribution function][cdf] for a [discrete uniform][discrete-uniform-distribution] distribution.
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for a [discrete uniform][discrete-uniform-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:discrete_uniform_cdf" align="center" raw="F(x)= \begin{cases} 0 & \text{for }x < a \\ \frac{\lfloor x \rfloor - a + 1}{b-a+1} & \text{for }a \le x < b \\ 1 & \text{for }x \ge b \end{cases}" alt="Cumulative distribution function for a discrete uniform distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F(x)= \begin{cases} 0 &amp; \text{for }x &lt; a \\ \frac{\lfloor x \rfloor - a + 1}{b-a+1} &amp; \text{for }a \le x &lt; b \\ 1 &amp; \text{for }x \ge b \end{cases}" data-equation="eq:discrete_uniform_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/discrete-uniform/logcdf/docs/img/equation_discrete_uniform_cdf.svg" alt="Cumulative distribution function for a discrete uniform distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `a` is the minimum support and `b` is the maximum support. The parameters must satisfy `a <= b`.
     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/discrete-uniform/logcdf' );
     50 ```
     51 
     52 #### logcdf( x, a, b )
     53 
     54 Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [discrete uniform][discrete-uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
     55 
     56 ```javascript
     57 var y = logcdf( 9.0, 0, 10 );
     58 // returns ~-0.095
     59 
     60 y = logcdf( 0.5, -2, 2 );
     61 // returns ~-0.511
     62 
     63 y = logcdf( -Infinity, 2, 4 );
     64 // returns -Infinity
     65 
     66 y = logcdf( Infinity, 2, 4 );
     67 // returns 0.0
     68 ```
     69 
     70 If `a` or `b` is not an integer value, the function returns `NaN`.
     71 
     72 ```javascript
     73 var y = logcdf( 2.0, 1, 5.5 );
     74 // returns NaN
     75 ```
     76 
     77 If provided `a > b`, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = logcdf( 0.5, 3, 2);
     81 // returns NaN
     82 ```
     83 
     84 If provided `NaN` for any parameter, the function returns `NaN`.
     85 
     86 ```javascript
     87 var y = logcdf( NaN, 0, 1 );
     88 // returns NaN
     89 
     90 y = logcdf( 0.0, NaN, 1 );
     91 // returns NaN
     92 
     93 y = logcdf( 0.0, 0, NaN );
     94 // returns NaN
     95 ```
     96 
     97 #### logcdf.factory( a, b )
     98 
     99 Returns a function for evaluating the natural logarithm of the [cumulative distribution function][cdf] of a [discrete uniform][discrete-uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
    100 
    101 ```javascript
    102 var myLogCDF = logcdf.factory( 0, 10 );
    103 var y = myLogCDF( 0.5 );
    104 // returns ~-2.398
    105 
    106 y = myLogCDF( 8.0 );
    107 // returns ~-0.201
    108 ```
    109 
    110 </section>
    111 
    112 <!-- /.usage -->
    113 
    114 <section class="examples">
    115 
    116 ## Examples
    117 
    118 <!-- eslint no-undef: "error" -->
    119 
    120 ```javascript
    121 var randint = require( '@stdlib/random/base/discrete-uniform' );
    122 var randu = require( '@stdlib/random/base/randu' );
    123 var logcdf = require( '@stdlib/stats/base/dists/discrete-uniform/logcdf' );
    124 
    125 var randa = randint.factory( 0, 10 );
    126 var randb = randint.factory();
    127 var a;
    128 var b;
    129 var x;
    130 var v;
    131 var i;
    132 
    133 for ( i = 0; i < 10; i++ ) {
    134     x = randu() * 15.0;
    135     a = randa();
    136     b = randb( a, a+randa() );
    137     v = logcdf( x, a, b );
    138     console.log( 'x: %d, a: %d, b: %d, ln(F(x;a,b)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
    139 }
    140 ```
    141 
    142 </section>
    143 
    144 <!-- /.examples -->
    145 
    146 <section class="links">
    147 
    148 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    149 
    150 [discrete-uniform-distribution]: https://en.wikipedia.org/wiki/Discrete_uniform_distribution
    151 
    152 </section>
    153 
    154 <!-- /.links -->