time-to-botec

Benchmark sampling in different programming languages
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README.md (4504B)

      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.
     18 
     19 -->
     20 
     21 # Entropy
     22 
     23 > [Erlang][erlang-distribution] distribution [differential entropy][entropy].
     24 
     25 <!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
     26 
     27 <section class="intro">
     28 
     29 The [differential entropy][entropy] for an [Erlang][erlang-distribution] random variable with shape `k` and rate `λ` is
     30 
     31 <!-- <equation class="equation" label="eq:erlang_entropy" align="center" raw="h\left( X \right) = (1\,-\,k)\psi (k)\,+\,\ln \left[{\frac {\Gamma (k)}{\lambda }}\right]\,+\,k" alt="Differential entropy for an Erlang distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="h\left( X \right) = (1\,-\,k)\psi (k)\,+\,\ln \left[{\frac {\Gamma (k)}{\lambda }}\right]\,+\,k" data-equation="eq:erlang_entropy">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/erlang/entropy/docs/img/equation_erlang_entropy.svg" alt="Differential entropy for an Erlang distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `Γ` and `Ψ` denote the [gamma][gamma-function] and [digamma][digamma] function, respectively.
     41 
     42 </section>
     43 
     44 <!-- /.intro -->
     45 
     46 <!-- Package usage documentation. -->
     47 
     48 <section class="usage">
     49 
     50 ## Usage
     51 
     52 ```javascript
     53 var entropy = require( '@stdlib/stats/base/dists/erlang/entropy' );
     54 ```
     55 
     56 #### entropy( k, lambda )
     57 
     58 Returns the [differential entropy][entropy] of an [Erlang][erlang-distribution] distribution with parameters shape `k` and rate `lambda` (in [nats][nats]).
     59 
     60 ```javascript
     61 var v = entropy( 1, 1.0 );
     62 // returns 1.0
     63 
     64 v = entropy( 4, 12.0 );
     65 // returns ~-0.462
     66 
     67 v = entropy( 8, 2.0 );
     68 // returns ~1.723
     69 ```
     70 
     71 If provided `NaN` as any argument, the function returns `NaN`.
     72 
     73 ```javascript
     74 var v = entropy( NaN, 2.0 );
     75 // returns NaN
     76 
     77 v = entropy( 2.0, NaN );
     78 // returns NaN
     79 ```
     80 
     81 If not provided a positive integer for `k`, the function returns `NaN`.
     82 
     83 ```javascript
     84 var v = entropy( 1.8, 1.0 );
     85 // returns NaN
     86 
     87 v = entropy( -1.0, 1.0 );
     88 // returns NaN
     89 ```
     90 
     91 If provided `lambda <= 0`, the function returns `NaN`.
     92 
     93 ```javascript
     94 var v = entropy( 2, 0.0 );
     95 // returns NaN
     96 
     97 v = entropy( 2, -1.0 );
     98 // returns NaN
     99 ```
    100 
    101 </section>
    102 
    103 <!-- /.usage -->
    104 
    105 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    106 
    107 <section class="notes">
    108 
    109 </section>
    110 
    111 <!-- /.notes -->
    112 
    113 <!-- Package usage examples. -->
    114 
    115 <section class="examples">
    116 
    117 ## Examples
    118 
    119 <!-- eslint no-undef: "error" -->
    120 
    121 ```javascript
    122 var randu = require( '@stdlib/random/base/randu' );
    123 var round = require( '@stdlib/math/base/special/round' );
    124 var EPS = require( '@stdlib/constants/float64/eps' );
    125 var entropy = require( '@stdlib/stats/base/dists/erlang/entropy' );
    126 
    127 var lambda;
    128 var k;
    129 var v;
    130 var i;
    131 
    132 for ( i = 0; i < 10; i++ ) {
    133     k = round( randu()*10.0 );
    134     lambda = ( randu()*10.0 ) + EPS;
    135     v = entropy( k, lambda );
    136     console.log( 'k: %d, λ: %d, h(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) );
    137 }
    138 ```
    139 
    140 </section>
    141 
    142 <!-- /.examples -->
    143 
    144 <!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    145 
    146 <section class="references">
    147 
    148 </section>
    149 
    150 <!-- /.references -->
    151 
    152 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    153 
    154 <section class="links">
    155 
    156 [erlang-distribution]: https://en.wikipedia.org/wiki/Erlang_distribution
    157 
    158 [entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29
    159 
    160 [nats]: https://en.wikipedia.org/wiki/Nat_%28unit%29
    161 
    162 [gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
    163 
    164 [digamma]: https://en.wikipedia.org/wiki/Digamma_function
    165 
    166 </section>
    167 
    168 <!-- /.links -->