time-to-botec

Benchmark sampling in different programming languages
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README.md (4038B)

      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 > [Arcsine][arcsine-distribution] distribution logarithm of [cumulative distribution function][cdf].
     24 
     25 <section class="intro">
     26 
     27 The [cumulative distribution function][cdf] for an [arcsine][arcsine-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:arcsine_cdf" align="center" raw="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" alt="Cumulative distribution function for an arcsine distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" data-equation="eq:arcsine_cdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/logcdf/docs/img/equation_arcsine_cdf.svg" alt="Cumulative distribution function for an arcsine distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 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 logcdf = require( '@stdlib/stats/base/dists/arcsine/logcdf' );
     50 ```
     51 
     52 #### logcdf( x, a, b )
     53 
     54 Evaluates the logarithm of the [cumulative distribution function][cdf] (CDF) for an [arcsine][arcsine-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
     55 
     56 ```javascript
     57 var y = logcdf( 9.0, 0.0, 10.0 );
     58 // returns ~-0.23
     59 
     60 y = logcdf( 0.5, 0.0, 2.0 );
     61 // returns ~-1.1
     62 
     63 y = logcdf( -Infinity, 2.0, 4.0 );
     64 // returns -Infinity
     65 
     66 y = logcdf( +Infinity, 2.0, 4.0 );
     67 // returns 0.0
     68 ```
     69 
     70 If provided `NaN` as any argument, the function returns `NaN`.
     71 
     72 ```javascript
     73 var y = logcdf( NaN, 0.0, 1.0 );
     74 // returns NaN
     75 
     76 y = logcdf( 0.0, NaN, 1.0 );
     77 // returns NaN
     78 
     79 y = logcdf( 0.0, 0.0, NaN );
     80 // returns NaN
     81 ```
     82 
     83 If provided `a >= b`, the function returns `NaN`.
     84 
     85 ```javascript
     86 var y = logcdf( 1.0, 2.5, 2.0 );
     87 // returns NaN
     88 ```
     89 
     90 #### logcdf.factory( a, b )
     91 
     92 Returns a function for evaluating the logarithm of the [cumulative distribution function][cdf] of an [arcsine][arcsine-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).
     93 
     94 ```javascript
     95 var mylogcdf = logcdf.factory( 0.0, 10.0 );
     96 var y = mylogcdf( 0.5 );
     97 // returns ~-1.941
     98 
     99 y = mylogcdf( 8.0 );
    100 // returns ~-0.35
    101 ```
    102 
    103 </section>
    104 
    105 <!-- /.usage -->
    106 
    107 <section class="notes">
    108 
    109 ## Notes
    110 
    111 -   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.
    112 
    113 </section>
    114 
    115 <!-- /.notes -->
    116 
    117 <section class="examples">
    118 
    119 ## Examples
    120 
    121 <!-- eslint no-undef: "error" -->
    122 
    123 ```javascript
    124 var randu = require( '@stdlib/random/base/randu' );
    125 var logcdf = require( '@stdlib/stats/base/dists/arcsine/logcdf' );
    126 
    127 var a;
    128 var b;
    129 var x;
    130 var y;
    131 var i;
    132 
    133 for ( i = 0; i < 25; i++ ) {
    134     x = ( randu()*20.0 ) - 10.0;
    135     a = ( randu()*20.0 ) - 20.0;
    136     b = a + ( randu()*40.0 );
    137     y = logcdf( x, a, b );
    138     console.log( 'x: %d, a: %d, b: %d, ln(F(x;a,b)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
    139 }
    140 ```
    141 
    142 </section>
    143 
    144 <!-- /.examples -->
    145 
    146 <section class="links">
    147 
    148 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
    149 
    150 [arcsine-distribution]: https://en.wikipedia.org/wiki/Arcsine_distribution
    151 
    152 </section>
    153 
    154 <!-- /.links -->