time-to-botec

Benchmark sampling in different programming languages
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README.md (4085B)

      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
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     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 Probability Mass Function
     22 
     23 > [Geometric][geometric-distribution] distribution logarithm of [probability mass function][pmf] (PMF).
     24 
     25 <section class="intro">
     26 
     27 The [probability mass function][pmf] (PMF) for a [geometric][geometric-distribution] random variable is defined as
     28 
     29 <!-- <equation class="equation" label="eq:geometric_pmf" align="center" raw="\Pr(X = x) = \begin{cases}(1-p)^{x}\,p & \text{ for } x=0,1,2,\ldots \\ 0 & \text{ otherwise } \end{cases}" alt="Probability mass function (PMF) for a geometric distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="\Pr(X = x) = \begin{cases}(1-p)^{x}\,p &amp; \text{ for } x=0,1,2,\ldots \\ 0 &amp; \text{ otherwise } \end{cases}" data-equation="eq:geometric_pmf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/geometric/logpmf/docs/img/equation_geometric_pmf.svg" alt="Probability mass function (PMF) for a geometric distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `0 <= p <= 1` is the success probability. The random variable `X` denotes the number of failures until the first success in a sequence of independent Bernoulli trials.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var logpmf = require( '@stdlib/stats/base/dists/geometric/logpmf' );
     50 ```
     51 
     52 #### logpmf( x, p )
     53 
     54 Evaluates the logarithm of the [probability mass function][pmf] (PMF) of a [geometric][geometric-distribution] distribution with success probability `0 <= p <= 1`.
     55 
     56 ```javascript
     57 var y = logpmf( 4.0, 0.3 );
     58 // returns ~-2.631
     59 
     60 y = logpmf( 2.0, 0.7 );
     61 // returns ~-2.765
     62 
     63 y = logpmf( -1.0, 0.5 );
     64 // returns -Infinity
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = logpmf( NaN, 0.0 );
     71 // returns NaN
     72 
     73 y = logpmf( 0.0, NaN );
     74 // returns NaN
     75 ```
     76 
     77 If provided a success probability `p` outside of the interval `[0,1]`, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = logpmf( 2.0, -1.0 );
     81 // returns NaN
     82 
     83 y = logpmf( 2.0, 1.5 );
     84 // returns NaN
     85 ```
     86 
     87 #### logpmf.factory( p )
     88 
     89 Returns a function for evaluating the logarithm of the [probability mass function][pmf] (PMF) of a [geometric][geometric-distribution] distribution with success probability `0 <= p <= 1`.
     90 
     91 ```javascript
     92 var mylogpmf = logpmf.factory( 0.5 );
     93 var y = mylogpmf( 3.0 );
     94 // returns ~-2.773
     95 
     96 y = mylogpmf( 1.0 );
     97 // returns ~-1.386
     98 ```
     99 
    100 </section>
    101 
    102 <!-- /.usage -->
    103 
    104 <section class="notes">
    105 
    106 ## Notes
    107 
    108 -   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.
    109 
    110 </section>
    111 
    112 <!-- /.notes -->
    113 
    114 <section class="examples">
    115 
    116 ## Examples
    117 
    118 <!-- eslint no-undef: "error" -->
    119 
    120 ```javascript
    121 var randu = require( '@stdlib/random/base/randu' );
    122 var round = require( '@stdlib/math/base/special/round' );
    123 var logpmf = require( '@stdlib/stats/base/dists/geometric/logpmf' );
    124 
    125 var p;
    126 var x;
    127 var y;
    128 var i;
    129 
    130 for ( i = 0; i < 10; i++ ) {
    131     x = round( randu() * 5.0 );
    132     p = randu();
    133     y = logpmf( x, p );
    134     console.log( 'x: %d, p: %d, ln( P( X = x; p ) ): %d', x, p.toFixed( 4 ), y.toFixed( 4 ) );
    135 }
    136 ```
    137 
    138 </section>
    139 
    140 <!-- /.examples -->
    141 
    142 <section class="links">
    143 
    144 [geometric-distribution]: https://en.wikipedia.org/wiki/Geometric_distribution
    145 
    146 [pmf]: https://en.wikipedia.org/wiki/Probability_mass_function
    147 
    148 </section>
    149 
    150 <!-- /.links -->