time-to-botec

Benchmark sampling in different programming languages
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README.md (3568B)

      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.
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     19 -->
     20 
     21 # Quantile Function
     22 
     23 > [Student's t][t-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [Student's t][t-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:t_quantile_function" align="center" raw="Q(p;\nu)\,=\,\inf\left\{ x\in \mathbb{R} : p \le F(x;\nu) \right\}" alt="Quantile function for a Student's t distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p;\nu)\,=\,\inf\left\{ x\in \mathbb{R} : p \le F(x;\nu) \right\}" data-equation="eq:t_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/t/quantile/docs/img/equation_t_quantile_function.svg" alt="Quantile function for a Student's t distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p <= 1`, where `v > 0` is the degrees of freedom.
     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/t/quantile' );
     50 ```
     51 
     52 #### quantile( p, v )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [Student's t][t-distribution] distribution with degrees of freedom `v`.
     55 
     56 ```javascript
     57 var y = quantile( 0.8, 1.0 );
     58 // returns ~1.376
     59 
     60 y = quantile( 0.1, 1.0 );
     61 // returns ~-3.078
     62 
     63 y = quantile( 0.5, 0.1 );
     64 // returns 0.0
     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 );
     71 // returns NaN
     72 
     73 y = quantile( -0.1, 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 );
     81 // returns NaN
     82 
     83 y = quantile( 0.0, NaN );
     84 // returns NaN
     85 ```
     86 
     87 If provided `v <= 0`, the function returns `NaN`.
     88 
     89 ```javascript
     90 var y = quantile( 0.4, -1.0 );
     91 // returns NaN
     92 
     93 y = quantile( 0.4, 0.0 );
     94 // returns NaN
     95 ```
     96 
     97 #### quantile.factory( v )
     98 
     99 Returns a function for evaluating the [quantile function][quantile-function] of an [Student's t][t-distribution] distribution with degrees of freedom `v`.
    100 
    101 ```javascript
    102 var myquantile = quantile.factory( 4.0 );
    103 
    104 var y = myquantile( 0.2 );
    105 // returns ~-0.941
    106 
    107 y = myquantile( 0.9 );
    108 // returns ~1.533
    109 ```
    110 
    111 </section>
    112 
    113 <!-- /.usage -->
    114 
    115 <section class="examples">
    116 
    117 ## Examples
    118 
    119 <!-- eslint no-undef: "error" -->
    120 
    121 ```javascript
    122 var randu = require( '@stdlib/random/base/randu' );
    123 var quantile = require( '@stdlib/stats/base/dists/t/quantile' );
    124 
    125 var v;
    126 var p;
    127 var y;
    128 var i;
    129 
    130 for ( i = 0; i < 10; i++ ) {
    131     p = randu();
    132     v = randu() * 10.0;
    133     y = quantile( p, v );
    134     console.log( 'p: %d, v: %d, Q(p;v): %d', p.toFixed( 4 ), v.toFixed( 4 ), y.toFixed( 4 ) );
    135 }
    136 ```
    137 
    138 </section>
    139 
    140 <!-- /.examples -->
    141 
    142 <section class="links">
    143 
    144 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    145 
    146 [t-distribution]: https://en.wikipedia.org/wiki/Student%27s_t-distribution
    147 
    148 </section>
    149 
    150 <!-- /.links -->