time-to-botec

Benchmark sampling in different programming languages
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README.md (3616B)

      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 > [Raised cosine][cosine-distribution] distribution [moment-generating function][mgf].
     24 
     25 <section class="intro">
     26 
     27 The [moment-generating function][mgf] for a [raised cosine][cosine-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:cosine_mgf" align="center" raw="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \frac{ \pi^{2} \sinh(st) }{ st(\pi^{2}+s^{2}t^{2}) } \,e^{\mu t}" alt="Moment-generating function for a raised cosine distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \frac{ \pi^{2} \sinh(st) }{ st(\pi^{2}+s^{2}t^{2}) } \,e^{\mu t}" data-equation="eq:cosine_mgf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/cosine/mgf/docs/img/equation_cosine_mgf.svg" alt="Moment-generating function for a raised cosine distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `μ` is the location parameter and `s > 0` is the scale parameter.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var mgf = require( '@stdlib/stats/base/dists/cosine/mgf' );
     50 ```
     51 
     52 #### mgf( t, mu, s )
     53 
     54 Evaluates the [moment-generating function][mgf] (MGF) for a [raised cosine][cosine-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter).
     55 
     56 ```javascript
     57 var y = mgf( 2.0, 0.0, 3.0 );
     58 // returns ~7.234
     59 
     60 y = mgf( 0.5, 0.0, 1.0 );
     61 // returns ~1.016
     62 
     63 y = mgf( -1.0, 4.0, 2.0 );
     64 // returns ~0.024
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = mgf( NaN, 0.0, 1.0 );
     71 // returns NaN
     72 
     73 y = mgf( 0.0, NaN, 1.0 );
     74 // returns NaN
     75 
     76 y = mgf( 0.0, 0.0, NaN );
     77 // returns NaN
     78 ```
     79 
     80 If provided `s <= 0`, the function returns `NaN`.
     81 
     82 ```javascript
     83 var y = mgf( 0.5, 0.0, -1.0 );
     84 // returns NaN
     85 
     86 y = mgf( 0.5, 0.0, 0.0 );
     87 // returns NaN
     88 ```
     89 
     90 #### mgf.factory( mu, s )
     91 
     92 Returns a function for evaluating the [moment-generating function][mgf] of a [raised cosine][cosine-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter).
     93 
     94 ```javascript
     95 var mymgf = mgf.factory( 10.0, 2.0 );
     96 
     97 var y = mymgf( 0.1 );
     98 // returns ~2.725
     99 ```
    100 
    101 </section>
    102 
    103 <!-- /.usage -->
    104 
    105 <section class="examples">
    106 
    107 ## Examples
    108 
    109 <!-- eslint no-undef: "error" -->
    110 
    111 ```javascript
    112 var randu = require( '@stdlib/random/base/randu' );
    113 var mgf = require( '@stdlib/stats/base/dists/cosine/mgf' );
    114 
    115 var mu;
    116 var s;
    117 var t;
    118 var y;
    119 var i;
    120 
    121 for ( i = 0; i < 10; i++ ) {
    122     t = randu() * 10.0;
    123     mu = randu() * 10.0;
    124     s = randu() * 10.0;
    125     y = mgf( t, mu, s );
    126     console.log( 't: %d, µ: %d, s: %d, M_X(t;µ,s): %d', t.toFixed( 4 ), mu.toFixed( 4 ), s.toFixed( 4 ), y.toFixed( 4 ) );
    127 }
    128 ```
    129 
    130 </section>
    131 
    132 <!-- /.examples -->
    133 
    134 <section class="links">
    135 
    136 [cosine-distribution]: https://en.wikipedia.org/wiki/Raised_cosine_distribution
    137 
    138 [mgf]: https://en.wikipedia.org/wiki/Moment-generating_function
    139 
    140 </section>
    141 
    142 <!-- /.links -->