time-to-botec

Benchmark sampling in different programming languages
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README.md (3956B)

      1 <!--
      2 
      3 @license Apache-2.0
      4 
      5 Copyright (c) 2018 The Stdlib Authors.
      6 
      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
     10 
     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.
     18 
     19 -->
     20 
     21 # Logarithm of Probability Density Function
     22 
     23 > Evaluate the natural logarithm of the [probability density function][pdf] (PDF) for a [chi-squared][chisquare-distribution] distribution.
     24 
     25 <section class="intro">
     26 
     27 The [probability density function][pdf] (PDF) for a [chi-squared][chisquare-distribution] random variable is
     28 
     29 <!-- <equation class="equation" label="eq:chisquare_pdf" align="center" raw="{\frac{1}{2^{\frac {k}{2}}\Gamma\left({\frac{k}{2}}\right)}}\;x^{{\frac {k}{2}}-1}e^{-{\frac {x}{2}}}" alt="Probability density function (PDF) for a chi-squared distribution."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="{\frac{1}{2^{\frac {k}{2}}\Gamma\left({\frac{k}{2}}\right)}}\;x^{{\frac {k}{2}}-1}e^{-{\frac {x}{2}}}" data-equation="eq:chisquare_pdf">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/chisquare/logpdf/docs/img/equation_chisquare_pdf.svg" alt="Probability density function (PDF) for a chi-squared distribution.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `k` is the degrees of freedom and `Γ` denotes the [gamma function][gamma-function].
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var logpdf = require( '@stdlib/stats/base/dists/chisquare/logpdf' );
     50 ```
     51 
     52 #### logpdf( x, k )
     53 
     54 Evaluates the natural logarithm of the [probability density function][pdf] (PDF) for a [chi-squared][chisquare-distribution] distribution with degrees of freedom `k`.
     55 
     56 ```javascript
     57 var y = logpdf( 0.1, 1.0 );
     58 // returns ~0.182
     59 
     60 y = logpdf( 0.5, 2.0 );
     61 // returns ~-0.943
     62 
     63 y = logpdf( -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 = logpdf( NaN, 1.0 );
     71 // returns NaN
     72 
     73 y = logpdf( 0.0, NaN );
     74 // returns NaN
     75 ```
     76 
     77 If provided `k < 0`, the function returns `NaN`.
     78 
     79 ```javascript
     80 var y = logpdf( 2.0, -2.0 );
     81 // returns NaN
     82 ```
     83 
     84 If provided `k = 0`, the function evaluates the [PDF][pdf] of a [degenerate distribution][degenerate-distribution] centered at `0`.
     85 
     86 ```javascript
     87 var y = logpdf( 2.0, 0.0 );
     88 // returns -Infinity
     89 
     90 y = logpdf( 0.0, 0.0 );
     91 // returns Infinity
     92 ```
     93 
     94 #### logpdf.factory( k )
     95 
     96 Returns a `function` for evaluating the [PDF][pdf] for a [chi-squared][chisquare-distribution] distribution with degrees of freedom `k`.
     97 
     98 ```javascript
     99 var myLogPDF = logpdf.factory( 6.0 );
    100 
    101 var y = myLogPDF( 3.0 );
    102 // returns ~-2.075
    103 
    104 y = myLogPDF( 1.0 );
    105 // returns ~-3.273
    106 ```
    107 
    108 </section>
    109 
    110 <!-- /.usage -->
    111 
    112 <section class="examples">
    113 
    114 ## Examples
    115 
    116 <!-- eslint no-undef: "error" -->
    117 
    118 ```javascript
    119 var randu = require( '@stdlib/random/base/randu' );
    120 var logpdf = require( '@stdlib/stats/base/dists/chisquare/logpdf' );
    121 
    122 var k;
    123 var x;
    124 var y;
    125 var i;
    126 
    127 for ( i = 0; i < 20; i++ ) {
    128     x = randu() * 10.0;
    129     k = randu() * 10.0;
    130     y = logpdf( x, k );
    131     console.log( 'x: %d, k: %d, ln(f(x;k)): %d', x.toFixed( 4 ), k.toFixed( 4 ), y.toFixed( 4 ) );
    132 }
    133 ```
    134 
    135 </section>
    136 
    137 <!-- /.examples -->
    138 
    139 <section class="links">
    140 
    141 [chisquare-distribution]: https://en.wikipedia.org/wiki/Chi-squared_distribution
    142 
    143 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
    144 
    145 [gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
    146 
    147 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function
    148 
    149 </section>
    150 
    151 <!-- /.links -->