time-to-botec

Benchmark sampling in different programming languages
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README.md (4096B)

      1 <!--
      2 
      3 @license Apache-2.0
      4 
      5 Copyright (c) 2018 The Stdlib Authors.
      6 
      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 > [F][f-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [F][f-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:f_quantile_function" align="center" raw="Q(p;d_1,d_2) = \,\inf\left\{ x\in [0,+\infty) : p \le F(x;d_1,d_2) \right\}" alt="Quantile function for an F distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p;d_1,d_2) = \,\inf\left\{ x\in [0,+\infty) : p \le F(x;d_1,d_2) \right\}" data-equation="eq:f_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/f/quantile/docs/img/equation_f_quantile_function.svg" alt="Quantile function for an F distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p < 1`, where `d1` is the numerator degrees of freedom, `d2` is the denominator degrees of freedom and `F` the cumulative distribution function (CDF) of the F distribution.
     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/f/quantile' );
     50 ```
     51 
     52 #### quantile( p, d1, d2 )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [F][f-distribution] distribution with parameters `d1` (numerator degrees of freedom) and `d2` (denominator degrees of freedom).
     55 
     56 ```javascript
     57 var y = quantile( 0.5, 1.0, 1.0 );
     58 // returns 1.0
     59 
     60 y = quantile( 0.2, 4.0, 2.0 );
     61 // returns ~0.405
     62 
     63 y = quantile( 0.8, 4.0, 2.0 );
     64 // returns ~4.236
     65 ```
     66 
     67 If provided a probability `p` outside the interval `[0,1]`, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = quantile( 1.9, 1.0, 1.0 );
     71 // returns NaN
     72 
     73 y = quantile( -0.1, 1.0, 1.0 );
     74 // returns NaN
     75 ```
     76 
     77 If provided `NaN` as any argument, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = quantile( NaN, 1.0, 1.0 );
     81 // returns NaN
     82 
     83 y = quantile( 0.0, NaN, 1.0 );
     84 // returns NaN
     85 
     86 y = quantile( 0.0, 1.0, NaN );
     87 // returns NaN
     88 ```
     89 
     90 If provided `d1 <= 0`, the function returns `NaN`.
     91 
     92 ```javascript
     93 var y = quantile( 0.4, -1.0, 1.0 );
     94 // returns NaN
     95 
     96 y = quantile( 0.4, 0.0, 1.0 );
     97 // returns NaN
     98 ```
     99 
    100 If provided `d2 <= 0`, the function returns `NaN`.
    101 
    102 ```javascript
    103 var y = quantile( 0.4, 1.0, -1.0 );
    104 // returns NaN
    105 
    106 y = quantile( 0.4, 1.0, 0.0 );
    107 // returns NaN
    108 ```
    109 
    110 #### quantile.factory( d1, d2 )
    111 
    112 Returns a function for evaluating the quantile function of a [F][f-distribution] distribution with parameters `d1` (numerator degrees of freedom) and `d2` (denominator degrees of freedom).
    113 
    114 ```javascript
    115 var myquantile = quantile.factory( 10.0, 2.0 );
    116 
    117 var y = myquantile( 0.2 );
    118 // returns ~0.527
    119 
    120 y = myquantile( 0.8 );
    121 // returns ~4.382
    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/f/quantile' );
    137 
    138 var d1;
    139 var d2;
    140 var p;
    141 var y;
    142 var i;
    143 
    144 for ( i = 0; i < 10; i++ ) {
    145     p = randu();
    146     d1 = randu() * 10.0;
    147     d2 = randu() * 10.0;
    148     y = quantile( p, d1, d2 );
    149     console.log( 'p: %d, d1: %d, d2: %d, Q(p;d1,d2): %d', p.toFixed( 4 ), d1.toFixed( 4 ), d2.toFixed( 4 ), y.toFixed( 4 ) );
    150 }
    151 ```
    152 
    153 </section>
    154 
    155 <!-- /.examples -->
    156 
    157 <section class="links">
    158 
    159 [f-distribution]: https://en.wikipedia.org/wiki/F_distribution
    160 
    161 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    162 
    163 </section>
    164 
    165 <!-- /.links -->