time-to-botec

Benchmark sampling in different programming languages
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README.md (4322B)

      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 > [Rayleigh][rayleigh-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 [Rayleigh][rayleigh-distribution] random variable is
     30 
     31 <!-- <equation class="equation" label="eq:rayleigh_mgf" align="center" raw="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 1+\sigma t\,e^{\sigma^2t^2/2}\sqrt{\frac{\pi}{2}} \left(\textrm{erf}\left(\frac{\sigma t}{\sqrt{2}}\right)\!+\!1\right)" alt="Moment-generating function (MGF) for a Rayleigh distribution."> -->
     32 
     33 <div class="equation" align="center" data-raw-text="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 1+\sigma t\,e^{\sigma^2t^2/2}\sqrt{\frac{\pi}{2}} \left(\textrm{erf}\left(\frac{\sigma t}{\sqrt{2}}\right)\!+\!1\right)" data-equation="eq:rayleigh_mgf">
     34     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/rayleigh/mgf/docs/img/equation_rayleigh_mgf.svg" alt="Moment-generating function (MGF) for a Rayleigh distribution.">
     35     <br>
     36 </div>
     37 
     38 <!-- </equation> -->
     39 
     40 where `sigma > 0` is the scale 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/rayleigh/mgf' );
     54 ```
     55 
     56 #### mgf( t, sigma )
     57 
     58 Evaluates the [moment-generating function][mgf] for a [Rayleigh][rayleigh-distribution] distribution with scale parameter `sigma`.
     59 
     60 ```javascript
     61 var y = mgf( 1.0, 3.0 );
     62 // returns ~678.508
     63 
     64 y = mgf( 1.0, 2.0 );
     65 // returns ~38.65
     66 
     67 y = mgf( -1.0, 4.0 );
     68 // returns ~-0.947
     69 ```
     70 
     71 If provided `NaN` as any argument, the function returns `NaN`.
     72 
     73 ```javascript
     74 var y = mgf( NaN, 1.0 );
     75 // returns NaN
     76 
     77 y = mgf( 0.0, NaN );
     78 // returns NaN
     79 ```
     80 
     81 If provided `sigma < 0`, the function returns `NaN`.
     82 
     83 ```javascript
     84 var y = mgf( 0.5, -1.0 );
     85 // returns NaN
     86 ```
     87 
     88 #### mgf.factory( sigma )
     89 
     90 Returns a function for evaluating the [moment-generating function][mgf] of a [Rayleigh][rayleigh-distribution] distribution with parameter `sigma` (scale parameter).
     91 
     92 ```javascript
     93 var myMGF = mgf.factory( 0.5 );
     94 var y = myMGF( 1.0 );
     95 // returns ~2.715
     96 
     97 y = myMGF( 0.5 );
     98 // returns ~1.888
     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 mgf = require( '@stdlib/stats/base/dists/rayleigh/mgf' );
    124 
    125 var sigma;
    126 var t;
    127 var y;
    128 var i;
    129 
    130 for ( i = 0; i < 10; i++ ) {
    131     t = randu();
    132     sigma = randu() * 5.0;
    133     y = mgf( t, sigma );
    134     console.log( 't: %d, σ: %d, M_X(t;σ): %d', t.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
    135 }
    136 ```
    137 
    138 </section>
    139 
    140 <!-- /.examples -->
    141 
    142 <!-- 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. -->
    143 
    144 <section class="references">
    145 
    146 </section>
    147 
    148 <!-- /.references -->
    149 
    150 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
    151 
    152 <section class="links">
    153 
    154 [rayleigh-distribution]: https://en.wikipedia.org/wiki/Rayleigh_distribution
    155 
    156 [mgf]: https://en.wikipedia.org/wiki/Moment-generating_function
    157 
    158 </section>
    159 
    160 <!-- /.links -->