time-to-botec

Benchmark sampling in different programming languages
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README.md (4092B)

      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 > [Chi-squared][chisquare-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [chi-squared][chisquare-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:chisquared_quantile_function" align="center" raw="Q(p; k) = 2 \cdot P^{-1}( p, k/2 )" alt="Quantile function for a chi-squared distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p; k) = 2 \cdot P^{-1}( p, k/2 )" data-equation="eq:chisquared_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/chisquare/quantile/docs/img/equation_chisquared_quantile_function.svg" alt="Quantile function for a chi-squared distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p < 1`, where `k` is the degrees of freedom and `P^{-1}` is the inverse of the lower, regularized [incomplete gamma function][@stlib/math/base/special/gammaincinv].
     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/chisquare/quantile' );
     50 ```
     51 
     52 #### quantile( p, k )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [chi-squared][chisquare-distribution] distribution with degrees of freedom `k`.
     55 
     56 ```javascript
     57 var y = quantile( 0.8, 1.0 );
     58 // returns ~1.642
     59 
     60 y = quantile( 0.5, 4.0 );
     61 // returns ~3.357
     62 
     63 y = quantile( 0.8, 0.1 );
     64 // returns ~0.014
     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( 0.2, NaN );
     84 // returns NaN
     85 ```
     86 
     87 If provided `k < 0`, the function returns `NaN`.
     88 
     89 ```javascript
     90 var y = quantile( 0.4, -1.0 );
     91 // returns NaN
     92 ```
     93 
     94 If provided `k = 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 );
     98 // returns 0.0
     99 
    100 y = quantile( 0.9, 0.0 );
    101 // returns 0.0
    102 ```
    103 
    104 #### quantile.factory( k )
    105 
    106 Returns a function for evaluating the [quantile function][quantile-function] of a [chi-squared][chisquare-distribution] distribution with degrees of freedom `k`.
    107 
    108 ```javascript
    109 var myquantile = quantile.factory( 0.4 );
    110 
    111 var y = myquantile( 0.9 );
    112 // returns ~1.21
    113 
    114 y = myquantile( 1.0 );
    115 // returns Infinity
    116 ```
    117 
    118 </section>
    119 
    120 <!-- /.usage -->
    121 
    122 <section class="examples">
    123 
    124 ## Examples
    125 
    126 <!-- eslint no-undef: "error" -->
    127 
    128 ```javascript
    129 var randu = require( '@stdlib/random/base/randu' );
    130 var quantile = require( '@stdlib/stats/base/dists/chisquare/quantile' );
    131 
    132 var k;
    133 var p;
    134 var y;
    135 var i;
    136 
    137 for ( i = 0; i < 20; i++ ) {
    138     p = randu();
    139     k = randu() * 10.0;
    140     y = quantile( p, k );
    141     console.log( 'p: %d, k: %d, Q(p;k): %d', p.toFixed( 4 ), k.toFixed( 4 ), y.toFixed( 4 ) );
    142 }
    143 ```
    144 
    145 </section>
    146 
    147 <!-- /.examples -->
    148 
    149 <section class="links">
    150 
    151 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    152 
    153 [chisquare-distribution]: https://en.wikipedia.org/wiki/Chi-squared_distribution
    154 
    155 [@stlib/math/base/special/gammaincinv]: https://github.com/stdlib-js/stdlib
    156 
    157 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    158 
    159 </section>
    160 
    161 <!-- /.links -->