time-to-botec

Benchmark sampling in different programming languages
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README.md (3986B)

      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 # Quantile Function
     22 
     23 > [Inverse gamma][inverse-gamma] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for an [inverse gamma][inverse-gamma] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:invgamma_quantile_function" align="center" raw="Q(p;\alpha,\beta) = \frac{\beta \, \Gamma(\alpha)}{\Gamma(\alpha, p)}" alt="Quantile function for an inverse gamma distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p;\alpha,\beta) = \frac{\beta \, \Gamma(\alpha)}{\Gamma(\alpha, p)}" data-equation="eq:invgamma_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/invgamma/quantile/docs/img/equation_invgamma_quantile_function.svg" alt="Quantile function for an inverse gamma distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p < 1`, where `alpha > 0` is the shape parameter and `beta > 0` is the scale parameter.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var quantile = require( '@stdlib/stats/base/dists/invgamma/quantile' );
     50 ```
     51 
     52 #### quantile( p, alpha, beta )
     53 
     54 Evaluates the [quantile function][quantile-function] for an [inverse gamma][inverse-gamma] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).
     55 
     56 ```javascript
     57 var y = quantile( 0.8, 2.0, 1.0 );
     58 // returns ~1.213
     59 
     60 y = quantile( 0.5, 4.0, 2.0 );
     61 // returns ~0.545
     62 ```
     63 
     64 If provided a probability `p` outside the interval `[0,1]`, the function returns `NaN`.
     65 
     66 ```javascript
     67 var y = quantile( 1.9, 1.0, 1.0 );
     68 // returns NaN
     69 
     70 y = quantile( -0.1, 1.0, 1.0 );
     71 // returns NaN
     72 ```
     73 
     74 If provided `NaN` as any argument, the function returns `NaN`.
     75 
     76 ```javascript
     77 var y = quantile( NaN, 1.0, 1.0 );
     78 // returns NaN
     79 
     80 y = quantile( 0.0, NaN, 1.0 );
     81 // returns NaN
     82 
     83 y = quantile( 0.0, 1.0, NaN );
     84 // returns NaN
     85 ```
     86 
     87 If provided `alpha <= 0`, the function returns `NaN`.
     88 
     89 ```javascript
     90 var y = quantile( 0.4, -1.0, 1.0 );
     91 // returns NaN
     92 ```
     93 
     94 If provided `beta <= 0`, the function returns `NaN`.
     95 
     96 ```javascript
     97 var y = quantile( 0.4, 1.0, -1.0 );
     98 // returns NaN
     99 ```
    100 
    101 #### quantile.factory( alpha, beta )
    102 
    103 Returns a function for evaluating the [quantile function][quantile-function] of an [inverse gamma][inverse-gamma] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).
    104 
    105 ```javascript
    106 var myquantile = quantile.factory( 2.0, 2.0 );
    107 var y = myquantile( 0.8 );
    108 // returns ~2.426
    109 
    110 y = myquantile( 0.4 );
    111 // returns ~0.989
    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 quantile = require( '@stdlib/stats/base/dists/invgamma/quantile' );
    127 
    128 var alpha;
    129 var beta;
    130 var p;
    131 var y;
    132 var i;
    133 
    134 for ( i = 0; i < 10; i++ ) {
    135     p = randu();
    136     alpha = randu() * 5.0;
    137     beta = randu() * 5.0;
    138     y = quantile( p, alpha, beta );
    139     console.log( 'p: %d, α: %d, β: %d, Q(p;α,β): %d', p.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 [inverse-gamma]: https://en.wikipedia.org/wiki/Inverse-gamma_distribution
    150 
    151 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    152 
    153 </section>
    154 
    155 <!-- /.links -->