time-to-botec

Benchmark sampling in different programming languages
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README.md (4414B)

      1 <!--
      2 
      3 @license Apache-2.0
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      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 > [Gamma][gamma-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [gamma][gamma-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:gamma_quantile_function" align="center" raw="Q(p;\alpha,\beta) = \frac{1}{\beta} P^{-1}\left( p, \alpha \right )" data-equation="eq:quantile_function" alt="Quantile function for a Gamma distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p;\alpha,\beta) = \frac{1}{\beta} P^{-1}\left( p, \alpha \right )" data-equation="eq:gamma_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/gamma/quantile/docs/img/equation_gamma_quantile_function.svg" alt="Quantile function for a Gamma distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p < 1`, where `alpha` is the shape parameter and `beta` is the rate parameter of the distribution. `P^{-1}` is the inverse of the lower regularized incomplete gamma function.
     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/gamma/quantile' );
     50 ```
     51 
     52 #### quantile( p, alpha, beta )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [gamma][gamma-distribution] 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 ~2.994
     59 
     60 y = quantile( 0.5, 4.0, 2.0 );
     61 // returns ~1.836
     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 `alpha = 0`, the function evaluates the [quantile function][quantile-function] of a [degenerate distribution][degenerate-distribution] centered at `0`.
     95 
     96 ```javascript
     97 var y = quantile( 0.3, 0.0, 2.0 );
     98 // returns 0.0
     99 
    100 y = quantile( 0.9, 0.0, 2.0 );
    101 // returns 0.0
    102 ```
    103 
    104 If provided `beta <= 0`, the function returns `NaN`.
    105 
    106 ```javascript
    107 var y = quantile( 0.4, 1.0, -1.0 );
    108 // returns NaN
    109 ```
    110 
    111 #### quantile.factory( alpha, beta )
    112 
    113 Returns a function for evaluating the [quantile function][quantile-function] of a [gamma][gamma-distribution] distribution with parameters `alpha` (shape parameter) and `beta` (rate parameter).
    114 
    115 ```javascript
    116 var myquantile = quantile.factory( 2.0, 2.0 );
    117 var y = myquantile( 0.8 );
    118 // returns ~1.497
    119 
    120 y = myquantile( 0.4 );
    121 // returns ~0.688
    122 ```
    123 
    124 </section>
    125 
    126 <!-- /.usage -->
    127 
    128 <section class="examples">
    129 
    130 ## Examples
    131 
    132 <!-- eslint no-undef: "error" -->
    133 
    134 ```javascript
    135 var randu = require( '@stdlib/random/base/randu' );
    136 var quantile = require( '@stdlib/stats/base/dists/gamma/quantile' );
    137 
    138 var alpha;
    139 var beta;
    140 var p;
    141 var y;
    142 var i;
    143 
    144 for ( i = 0; i < 20; i++ ) {
    145     p = randu();
    146     alpha = randu() * 5.0;
    147     beta = randu() * 5.0;
    148     y = quantile( p, alpha, beta );
    149     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 ) );
    150 }
    151 ```
    152 
    153 </section>
    154 
    155 <!-- /.examples -->
    156 
    157 <section class="links">
    158 
    159 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    160 
    161 [gamma-distribution]: https://en.wikipedia.org/wiki/Gamma_distribution
    162 
    163 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    164 
    165 </section>
    166 
    167 <!-- /.links -->