time-to-botec

Benchmark sampling in different programming languages
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README.md (4130B)

      1 <!--
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      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
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     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 > [Discrete uniform][discrete-uniform-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [discrete uniform][discrete-uniform-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:discrete_uniform_quantile_function" align="center" raw="Q(p) = a + \lfloor p \cdot ( b - a + 1 ) \rfloor" alt="Quantile function for a discrete uniform distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p) = a + \lfloor p \cdot ( b - a + 1 ) \rfloor" data-equation="eq:discrete_uniform_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/discrete-uniform/quantile/docs/img/equation_discrete_uniform_quantile_function.svg" alt="Quantile function for a discrete uniform distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p <= 1`, where `a` is the minimum support and `b` is the maximum support. The parameters must satisfy `a <= b`.
     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/discrete-uniform/quantile' );
     50 ```
     51 
     52 #### quantile( p, a, b )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [discrete uniform][discrete-uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
     55 
     56 ```javascript
     57 var y = quantile( 0.8, 0, 1 );
     58 // returns 1
     59 
     60 y = quantile( 0.5, 0, 10 );
     61 // returns 5
     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, 0, 2 );
     68 // returns NaN
     69 
     70 y = quantile( -0.1, 0, 2 );
     71 // returns NaN
     72 ```
     73 
     74 If `a` or `b` is not an integer value, the function returns `NaN`.
     75 
     76 ```javascript
     77 var y = quantile( 0.2, 1, 5.5 );
     78 // returns NaN
     79 ```
     80 
     81 If provided `a > b`, the function returns `NaN`.
     82 
     83 ```javascript
     84 var y = quantile( 0.4, 2, 1 );
     85 // returns NaN
     86 ```
     87 
     88 If provided `NaN` as any argument, the function returns `NaN`.
     89 
     90 ```javascript
     91 var y = quantile( NaN, 0.0, 1.0 );
     92 // returns NaN
     93 
     94 y = quantile( 0.0, NaN, 1.0 );
     95 // returns NaN
     96 
     97 y = quantile( 0.0, 0.0, NaN );
     98 // returns NaN
     99 ```
    100 
    101 #### quantile.factory( a, b )
    102 
    103 Returns a function for evaluating the quantile function of a [discrete uniform][discrete-uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
    104 
    105 ```javascript
    106 var myquantile = quantile.factory( 0, 4 );
    107 var y = myquantile( 0.8 );
    108 // returns 4
    109 
    110 y = myquantile( 0.3 );
    111 // returns 1
    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 randint = require( '@stdlib/random/base/discrete-uniform' );
    126 var randu = require( '@stdlib/random/base/randu' );
    127 var quantile = require( '@stdlib/stats/base/dists/discrete-uniform/quantile' );
    128 
    129 var randa = randint.factory( 0, 5 );
    130 var randb = randint.factory();
    131 var a;
    132 var b;
    133 var p;
    134 var v;
    135 var i;
    136 
    137 for ( i = 0; i < 10; i++ ) {
    138     p = randu();
    139     a = randa();
    140     b = randb( a, a+randa() );
    141     v = quantile( p, a, b );
    142     console.log( 'p: %d, a: %d, b: %d, Q(p;a,b): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
    143 }
    144 ```
    145 
    146 </section>
    147 
    148 <!-- /.examples -->
    149 
    150 <section class="links">
    151 
    152 [discrete-uniform-distribution]: https://en.wikipedia.org/wiki/Discrete_uniform_distribution
    153 
    154 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    155 
    156 </section>
    157 
    158 <!-- /.links -->