time-to-botec

Benchmark sampling in different programming languages
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README.md (3923B)

      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.
     18 
     19 -->
     20 
     21 # Logarithm of Cumulative Distribution Function
     22 
     23 > [Geometric][geometric-distribution] distribution logarithm of [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for a [geometric][geometric-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:geometric_cdf" align="center" raw="F(x;p)= \begin{cases} 0 & \text{ for } x < 0 \\ 1-(1 - p)^{\left\lfloor x \right\rfloor+1} & \text{ otherwise} \end{cases}" alt="Cumulative distribution function for a geometric distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F(x;p)= \begin{cases} 0 &amp; \text{ for } x &lt; 0 \\ 1-(1 - p)^{\left\lfloor x \right\rfloor+1} &amp; \text{ otherwise} \end{cases}" data-equation="eq:geometric_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/geometric/logcdf/docs/img/equation_geometric_cdf.svg" alt="Cumulative distribution function for a geometric distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `0 <= p <= 1` is the success probability. `x` denotes the number of _failures_ before the first success.
     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/geometric/logcdf' );
     50 ```
     51 
     52 #### logcdf( x, p )
     53 
     54 Evaluates the logarithm of the [cumulative distribution function][cdf] for a [geometric][geometric-distribution] distribution with success probability `p`.
     55 
     56 ```javascript
     57 var y = logcdf( 2.0, 0.5 );
     58 // returns ~-0.134
     59 
     60 y = logcdf( 2.0, 0.1 );
     61 // returns ~-1.306
     62 ```
     63 
     64 If provided `NaN` as any argument, the function returns `NaN`.
     65 
     66 ```javascript
     67 var y = logcdf( NaN, 0.5 );
     68 // returns NaN
     69 
     70 y = logcdf( 0.0, NaN );
     71 // returns NaN
     72 ```
     73 
     74 If provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.
     75 
     76 ```javascript
     77 var y = logcdf( 2.0, -1.0 );
     78 // returns NaN
     79 
     80 y = logcdf( 2.0, 1.5 );
     81 // returns NaN
     82 ```
     83 
     84 #### logcdf.factory( p )
     85 
     86 Returns a function for evaluating the logarithm of the [cumulative distribution function][cdf] of a [geometric][geometric-distribution] distribution with success probability `p`
     87 
     88 ```javascript
     89 var mylogcdf = logcdf.factory( 0.5 );
     90 var y = mylogcdf( 3.0 );
     91 // returns ~-0.065
     92 
     93 y = mylogcdf( 1.0 );
     94 // returns ~-0.288
     95 ```
     96 
     97 </section>
     98 
     99 <!-- /.usage -->
    100 
    101 <section class="notes">
    102 
    103 ## Notes
    104 
    105 -   In virtually all cases, using the `logpmf` or `logcdf` functions is preferable to manually computing the logarithm of the `pmf` or `cdf`, respectively, since the latter is prone to overflow and underflow.
    106 
    107 </section>
    108 
    109 <!-- /.notes -->
    110 
    111 <section class="examples">
    112 
    113 ## Examples
    114 
    115 <!-- eslint no-undef: "error" -->
    116 
    117 ```javascript
    118 var randu = require( '@stdlib/random/base/randu' );
    119 var logcdf = require( '@stdlib/stats/base/dists/geometric/logcdf' );
    120 
    121 var p;
    122 var x;
    123 var y;
    124 var i;
    125 
    126 for ( i = 0; i < 10; i++ ) {
    127     x = randu() * 5.0;
    128     p = randu();
    129     y = logcdf( x, p );
    130     console.log( 'x: %d, p: %d, ln(F(x;p)): %d', x.toFixed( 4 ), p.toFixed( 4 ), y.toFixed( 4 ) );
    131 }
    132 ```
    133 
    134 </section>
    135 
    136 <!-- /.examples -->
    137 
    138 <section class="links">
    139 
    140 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    141 
    142 [geometric-distribution]: https://en.wikipedia.org/wiki/Geometric_distribution
    143 
    144 </section>
    145 
    146 <!-- /.links -->