time-to-botec

Benchmark sampling in different programming languages
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README.md (4143B)

      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 # Moment-Generating Function
     22 
     23 > [Poisson][poisson-distribution] distribution moment-generating function (MGF).
     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 [moment-generating function][mgf] for a [Poisson][poisson-distribution] random variable is
     30 
     31 <!-- <equation class="equation" label="eq:poisson_mgf_function" align="center" raw="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \exp\{ \mu t + \frac{1}{2}\sigma^2t^2 \}" alt="Moment-generating function (MGF) for a Poisson distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \exp\{ \mu t + \frac{1}{2}\sigma^2t^2 \}" data-equation="eq:poisson_mgf_function">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/poisson/mgf/docs/img/equation_poisson_mgf_function.svg" alt="Moment-generating function (MGF) for a Poisson distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `lambda > 0` is the mean parameter.
     41 
     42 </section>
     43 
     44 <!-- /.intro -->
     45 
     46 <!-- Package usage documentation. -->
     47 
     48 <section class="usage">
     49 
     50 ## Usage
     51 
     52 ```javascript
     53 var mgf = require( '@stdlib/stats/base/dists/poisson/mgf' );
     54 ```
     55 
     56 #### mgf( t, lambda )
     57 
     58 Evaluates the moment-generating function ([MGF][mgf]) for a [Poisson][poisson-distribution] distribution with parameter `lambda` (mean).
     59 
     60 ```javascript
     61 var y = mgf( 1.0, 1.5 );
     62 // returns ~13.163
     63 
     64 y = mgf( 0.5, 0.5 );
     65 // returns ~1.383
     66 ```
     67 
     68 If provided `NaN` as any argument, the function returns `NaN`.
     69 
     70 ```javascript
     71 var y = mgf( NaN, 0.5 );
     72 // returns NaN
     73 
     74 y = mgf( 0.0, NaN );
     75 // returns NaN
     76 ```
     77 
     78 If provided `lambda <= 0`, the function returns `NaN`.
     79 
     80 ```javascript
     81 var y = mgf( -2.0, -1.0 );
     82 // returns NaN
     83 
     84 y = mgf( 0.1, 0.0 );
     85 // returns NaN
     86 ```
     87 
     88 #### mgf.factory( lambda )
     89 
     90 Returns a function for evaluating the [moment-generating function][mgf] of a [Poisson][poisson-distribution] distribution with parameter `lambda` (mean).
     91 
     92 ```javascript
     93 var mymgf = mgf.factory( 2.0 );
     94 var y = mymgf( 0.1 );
     95 // returns ~1.234
     96 ```
     97 
     98 </section>
     99 
    100 <!-- /.usage -->
    101 
    102 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    103 
    104 <section class="notes">
    105 
    106 </section>
    107 
    108 <!-- /.notes -->
    109 
    110 <!-- Package usage examples. -->
    111 
    112 <section class="examples">
    113 
    114 ## Examples
    115 
    116 <!-- eslint no-undef: "error" -->
    117 
    118 ```javascript
    119 var randu = require( '@stdlib/random/base/randu' );
    120 var mgf = require( '@stdlib/stats/base/dists/poisson/mgf' );
    121 
    122 var lambda;
    123 var t;
    124 var y;
    125 var i;
    126 
    127 for ( i = 0; i < 10; i++ ) {
    128     t = randu() * 5.0;
    129     lambda = randu() * 5.0;
    130     y = mgf( t, lambda );
    131     console.log( 'x: %d, λ: %d, M_X(t;λ): %d', t.toFixed( 4 ), lambda.toFixed( 4 ), y.toFixed( 4 ) );
    132 }
    133 ```
    134 
    135 </section>
    136 
    137 <!-- /.examples -->
    138 
    139 <!-- 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. -->
    140 
    141 <section class="references">
    142 
    143 </section>
    144 
    145 <!-- /.references -->
    146 
    147 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    148 
    149 <section class="links">
    150 
    151 [poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution
    152 
    153 [mgf]: https://en.wikipedia.org/wiki/Moment-generating_function
    154 
    155 </section>
    156 
    157 <!-- /.links -->