time-to-botec

Benchmark sampling in different programming languages
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README.md (3948B)

      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 > [Lognormal][lognormal-distribution] distribution [quantile function][quantile-function].
     24 
     25 <section class="intro">
     26 
     27 The [quantile function][quantile-function] for a [lognormal][lognormal-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:quantile_function" align="center" raw="Q(p;\mu,\sigma)=\exp\left( \mu + \sigma \Phi^{-1}(p) \right )" alt="Quantile function for a lognormal distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="Q(p;\mu,\sigma)=\exp\left( \mu + \sigma \Phi^{-1}(p) \right )" data-equation="eq:quantile_function">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/lognormal/quantile/docs/img/equation_quantile_function.svg" alt="Quantile function for a lognormal distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 for `0 <= p < 1`, where `mu` is the location parameter and `sigma > 0` is the scale parameter.
     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/lognormal/quantile' );
     50 ```
     51 
     52 #### quantile( p, mu, sigma )
     53 
     54 Evaluates the [quantile function][quantile-function] for a [lognormal][lognormal-distribution] distribution with parameters `mu` (location parameter) and `sigma` (scale parameter).
     55 
     56 ```javascript
     57 var y = quantile( 0.5, 0.0, 1.0 );
     58 // returns 1.0
     59 
     60 y = quantile( 0.5, 4.0, 1.0 );
     61 // returns ~54.598
     62 
     63 y = quantile( 0.8, 4.0, 1.0 );
     64 // returns ~126.675
     65 
     66 y = quantile( 0.8, 4.0, 4.0 );
     67 // returns ~1582.063
     68 ```
     69 
     70 If provided a probability `p` outside the interval `[0,1]`, the function returns `NaN`.
     71 
     72 ```javascript
     73 var y = quantile( 1.9, 0.0, 1.0 );
     74 // returns NaN
     75 
     76 y = quantile( -0.1, 0.0, 1.0 );
     77 // returns NaN
     78 ```
     79 
     80 If provided `NaN` as any argument, the function returns `NaN`.
     81 
     82 ```javascript
     83 var y = quantile( NaN, 0.0, 1.0 );
     84 // returns NaN
     85 
     86 y = quantile( 0.0, NaN, 1.0 );
     87 // returns NaN
     88 
     89 y = quantile( 0.0, 0.0, NaN );
     90 // returns NaN
     91 ```
     92 
     93 If provided `sigma <= 0`, the function returns `NaN`.
     94 
     95 ```javascript
     96 var y = quantile( 0.4, 0.0, -1.0 );
     97 // returns NaN
     98 
     99 y = quantile( 0.4, 0.0, 0.0 );
    100 // returns NaN
    101 ```
    102 
    103 #### quantile.factory( mu, sigma )
    104 
    105 Returns a function for evaluating the [quantile function][quantile-function] of a [lognormal][lognormal-distribution] distribution with parameters `mu` and `sigma`.
    106 
    107 ```javascript
    108 var myquantile = quantile.factory( 4.0, 2.0 );
    109 
    110 var y = myquantile( 0.2 );
    111 // returns ~10.143
    112 
    113 y = myquantile( 0.8 );
    114 // returns ~293.901
    115 ```
    116 
    117 </section>
    118 
    119 <!-- /.usage -->
    120 
    121 <section class="examples">
    122 
    123 ## Examples
    124 
    125 <!-- eslint no-undef: "error" -->
    126 
    127 ```javascript
    128 var randu = require( '@stdlib/random/base/randu' );
    129 var quantile = require( '@stdlib/stats/base/dists/lognormal/quantile' );
    130 
    131 var sigma;
    132 var mu;
    133 var p;
    134 var y;
    135 var i;
    136 
    137 for ( i = 0; i < 10; i++ ) {
    138     p = randu();
    139     mu = (randu() * 10.0) - 5.0;
    140     sigma = randu() * 20.0;
    141     y = quantile( p, mu, sigma );
    142     console.log( 'p: %d, µ: %d, σ: %d, Q(p;µ,σ): %d', p.toFixed( 4 ), mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
    143 }
    144 ```
    145 
    146 </section>
    147 
    148 <!-- /.examples -->
    149 
    150 <section class="links">
    151 
    152 [lognormal-distribution]: https://en.wikipedia.org/wiki/Lognormal_distribution
    153 
    154 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function
    155 
    156 </section>
    157 
    158 <!-- /.links -->