time-to-botec

Benchmark sampling in different programming languages
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README.md (3995B)

      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.
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     19 -->
     20 
     21 # Cumulative Distribution Function
     22 
     23 > [Inverse Gamma][inverse-gamma] distribution [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for an [inverse gamma][inverse-gamma] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:invgamma_cdf" align="center" raw="F(x; \alpha, \beta) = \frac{\Gamma\left(\alpha,\frac{\beta}{x}\right)}{\Gamma(\alpha)} = Q\left(\frac{\beta}{x},\alpha\right)" alt="Cumulative distribution function for a Inverse Gamma distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F(x; \alpha, \beta) = \frac{\Gamma\left(\alpha,\frac{\beta}{x}\right)}{\Gamma(\alpha)} = Q\left(\frac{\beta}{x},\alpha\right)" data-equation="eq:invgamma_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/invgamma/cdf/docs/img/equation_invgamma_cdf.svg" alt="Cumulative distribution function for a Inverse Gamma distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `alpha > 0` is the shape parameter and `beta > 0` is the scale parameter. `Q` is the upper regularized incomplete gamma function.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var cdf = require( '@stdlib/stats/base/dists/invgamma/cdf' );
     50 ```
     51 
     52 #### cdf( x, alpha, beta )
     53 
     54 Evaluates the [cumulative distribution function][cdf] (CDF) for an [inverse gamma][inverse-gamma] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).
     55 
     56 ```javascript
     57 var y = cdf( 2.0, 1.0, 1.0 );
     58 // returns ~0.607
     59 
     60 y = cdf( 2.0, 3.0, 1.0 );
     61 // returns ~0.986
     62 
     63 y = cdf( -1.0, 2.0, 2.0 );
     64 // returns 0.0
     65 
     66 y = cdf( -Infinity, 4.0, 2.0 );
     67 // returns 0.0
     68 
     69 y = cdf( +Infinity, 4.0, 2.0 );
     70 // returns 1.0
     71 ```
     72 
     73 If provided `NaN` as any argument, the function returns `NaN`.
     74 
     75 ```javascript
     76 var y = cdf( NaN, 1.0, 1.0 );
     77 // returns NaN
     78 
     79 y = cdf( 0.0, NaN, 1.0 );
     80 // returns NaN
     81 
     82 y = cdf( 0.0, 1.0, NaN );
     83 // returns NaN
     84 ```
     85 
     86 If provided `alpha <= 0`, the function returns `NaN`.
     87 
     88 ```javascript
     89 var y = cdf( 2.0, -1.0, 0.5 );
     90 // returns NaN
     91 ```
     92 
     93 If provided `beta <= 0`, the function returns `NaN`.
     94 
     95 ```javascript
     96 var y = cdf( 2.0, 0.5, -1.0 );
     97 // returns NaN
     98 ```
     99 
    100 #### cdf.factory( alpha, beta )
    101 
    102 Returns a function for evaluating the [cumulative distribution function][cdf] for an [inverse gamma][inverse-gamma] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).
    103 
    104 ```javascript
    105 var mycdf = cdf.factory( 0.5, 0.1 );
    106 
    107 var y = mycdf( 12.0 );
    108 // returns ~0.897
    109 
    110 y = mycdf( 8.0 );
    111 // returns ~0.874
    112 ```
    113 
    114 </section>
    115 
    116 <!-- /.usage -->
    117 
    118 <section class="examples">
    119 
    120 ## Examples
    121 
    122 <!-- eslint no-undef: "error" -->
    123 
    124 ```javascript
    125 var randu = require( '@stdlib/random/base/randu' );
    126 var cdf = require( '@stdlib/stats/base/dists/invgamma/cdf' );
    127 
    128 var alpha;
    129 var beta;
    130 var x;
    131 var y;
    132 var i;
    133 
    134 for ( i = 0; i < 10; i++ ) {
    135     x = randu() * 2.0;
    136     alpha = randu() * 5.0;
    137     beta = randu() * 5.0;
    138     y = cdf( x, alpha, beta );
    139     console.log( 'x: %d, α: %d, β: %d, F(x;α,β): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
    140 }
    141 ```
    142 
    143 </section>
    144 
    145 <!-- /.examples -->
    146 
    147 <section class="links">
    148 
    149 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    150 
    151 [inverse-gamma]: https://en.wikipedia.org/wiki/Inverse-gamma_distribution
    152 
    153 </section>
    154 
    155 <!-- /.links -->