time-to-botec

Benchmark sampling in different programming languages
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README.md (4059B)

      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
     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 > [Weibull][weibull-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [Weibull][weibull-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:weibull_quantile_function" align="center" raw="Q(p;k,\lambda) = \lambda {(-\ln(1-p))}^{1/k}" alt="Quantile function for a Weibull distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p;k,\lambda) = \lambda {(-\ln(1-p))}^{1/k}" data-equation="eq:weibull_quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/weibull/quantile/docs/img/equation_weibull_quantile_function.svg" alt="Quantile function for a Weibull distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p < 1`, where `lambda > 0` is the [shape parameter][shape] and `k > 0` is the [scale parameter][scale].
     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/weibull/quantile' );
     50 ```
     51 
     52 #### quantile( p, k, lambda )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [Weibull][weibull-distribution] distribution with [shape parameter][shape] `k` and [scale parameter][scale] `lambda`.
     55 
     56 ```javascript
     57 var y = quantile( 0.5, 1.0, 1.0 );
     58 // returns ~0.693
     59 
     60 y = quantile( 0.2, 2.0, 4.0 );
     61 // returns ~1.89
     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 `k <= 0`, the function returns `NaN`.
     88 
     89 ```javascript
     90 var y = quantile( 0.4, -1.0, 1.0 );
     91 // returns NaN
     92 
     93 y = quantile( 0.4, 0.0, 1.0 );
     94 // returns NaN
     95 ```
     96 
     97 If provided `lambda <= 0`, the function returns `NaN`.
     98 
     99 ```javascript
    100 var y = quantile( 0.4, 1.0, -1.0 );
    101 // returns NaN
    102 
    103 y = quantile( 0.4, 1.0, 0.0 );
    104 // returns NaN
    105 ```
    106 
    107 #### quantile.factory( k, lambda )
    108 
    109 Returns a function for evaluating the quantile function of a [Weibull][weibull-distribution] distribution with [shape parameter][shape] `k` and [scale parameter][scale] `lambda`.
    110 
    111 ```javascript
    112 var myquantile = quantile.factory( 2.0, 10.0 );
    113 
    114 var y = myquantile( 0.2 );
    115 // returns ~4.724
    116 
    117 y = myquantile( 0.8 );
    118 // returns ~12.686
    119 ```
    120 
    121 </section>
    122 
    123 <!-- /.usage -->
    124 
    125 <section class="examples">
    126 
    127 ## Examples
    128 
    129 <!-- eslint no-undef: "error" -->
    130 
    131 ```javascript
    132 var randu = require( '@stdlib/random/base/randu' );
    133 var quantile = require( '@stdlib/stats/base/dists/weibull/quantile' );
    134 
    135 var lambda;
    136 var k;
    137 var p;
    138 var y;
    139 var i;
    140 
    141 for ( i = 0; i < 10; i++ ) {
    142     p = randu();
    143     lambda = randu() * 10.0;
    144     k = randu() * 10.0;
    145     y = quantile( p, k, lambda );
    146     console.log( 'p: %d, k: %d, λ: %d, Q(p;k,λ): %d', p, k, lambda, y );
    147 }
    148 ```
    149 
    150 </section>
    151 
    152 <!-- /.examples -->
    153 
    154 <section class="links">
    155 
    156 [weibull-distribution]: https://en.wikipedia.org/wiki/Weibull_distribution
    157 
    158 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    159 
    160 [shape]: https://en.wikipedia.org/wiki/Shape_parameter
    161 
    162 [scale]: https://en.wikipedia.org/wiki/Scale_parameter
    163 
    164 </section>
    165 
    166 <!-- /.links -->