time-to-botec

Benchmark sampling in different programming languages
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README.md (4218B)

      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 # Logarithm of Cumulative Distribution Function
     22 
     23 > [Rayleigh][rayleigh-distribution] distribution logarithm of [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for a [Rayleigh][rayleigh-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:rayleigh_cdf" align="center" raw="F(x;\sigma) = \begin{cases} 0 & \text{ for } x < 0 \\ 1 - e^{-x^2/2\sigma^2} & \text{ for } x \ge 0 \end{cases}" alt="Cumulative distribution function for a Rayleigh distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F(x;\sigma) = \begin{cases} 0 &amp; \text{ for } x &lt; 0 \\ 1 - e^{-x^2/2\sigma^2} &amp; \text{ for } x \ge 0 \end{cases}" data-equation="eq:rayleigh_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/rayleigh/logcdf/docs/img/equation_rayleigh_cdf.svg" alt="Cumulative distribution function for a Rayleigh distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `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 logcdf = require( '@stdlib/stats/base/dists/rayleigh/logcdf' );
     50 ```
     51 
     52 #### logcdf( x, sigma )
     53 
     54 Evaluates the logarithm of the [cumulative distribution function][cdf] for a [Rayleigh][rayleigh-distribution] distribution with scale parameter `sigma`.
     55 
     56 ```javascript
     57 var y = logcdf( 2.0, 3.0 );
     58 // returns ~-1.613
     59 
     60 y = logcdf( 1.0, 2.0 );
     61 // returns ~-2.141
     62 
     63 y = logcdf( -1.0, 4.0 );
     64 // returns -Infinity
     65 ```
     66 
     67 If provided `NaN` as any argument, the function returns `NaN`.
     68 
     69 ```javascript
     70 var y = logcdf( NaN, 1.0 );
     71 // returns NaN
     72 
     73 y = logcdf( 0.0, NaN );
     74 // returns NaN
     75 ```
     76 
     77 If provided `sigma < 0`, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = logcdf( 2.0, -1.0 );
     81 // returns NaN
     82 ```
     83 
     84 If provided `sigma = 0`, the function evaluates the logarithm of the [CDF][cdf] for a [degenerate distribution][degenerate-distribution] centered at `0`.
     85 
     86 ```javascript
     87 var y = logcdf( -2.0, 0.0 );
     88 // returns -Infinity
     89 
     90 y = logcdf( 0.0, 0.0 );
     91 // returns 0.0
     92 
     93 y = logcdf( 2.0, 0.0 );
     94 // returns 0.0
     95 ```
     96 
     97 #### logcdf.factory( sigma )
     98 
     99 Returns a function for evaluating the logarithm of the [cumulative distribution function][cdf] of a [Rayleigh][rayleigh-distribution] distribution with parameter `sigma` (scale parameter).
    100 
    101 ```javascript
    102 var mylogCDF = logcdf.factory( 0.5 );
    103 y = mylogCDF( 1.0 );
    104 // returns ~-0.145
    105 
    106 y = mylogCDF( 0.5 );
    107 // returns ~-0.933
    108 ```
    109 
    110 </section>
    111 
    112 <!-- /.usage -->
    113 
    114 <section class="notes">
    115 
    116 ## Notes
    117 
    118 -   In virtually all cases, using the `logpdf` or `logcdf` functions is preferable to manually computing the logarithm of the `pdf` or `cdf`, respectively, since the latter is prone to overflow and underflow.
    119 
    120 </section>
    121 
    122 <!-- /.notes -->
    123 
    124 <section class="examples">
    125 
    126 ## Examples
    127 
    128 <!-- eslint no-undef: "error" -->
    129 
    130 ```javascript
    131 var randu = require( '@stdlib/random/base/randu' );
    132 var logcdf = require( '@stdlib/stats/base/dists/rayleigh/logcdf' );
    133 
    134 var sigma;
    135 var x;
    136 var y;
    137 var i;
    138 
    139 for ( i = 0; i < 10; i++ ) {
    140     x = randu() * 10.0;
    141     sigma = randu() * 10.0;
    142     y = logcdf( x, sigma );
    143     console.log( 'x: %d, σ: %d, log(F(x;σ)): %d', x.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
    144 }
    145 ```
    146 
    147 </section>
    148 
    149 <!-- /.examples -->
    150 
    151 <section class="links">
    152 
    153 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    154 
    155 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    156 
    157 [rayleigh-distribution]: https://en.wikipedia.org/wiki/Rayleigh_distribution
    158 
    159 </section>
    160 
    161 <!-- /.links -->