time-to-botec

README.md (3816B)

---

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 # Logarithm of Probability Density Function
 
 > Evaluate the natural logarithm of the [probability density function][pdf] (PDF) for a [chi][chi-distribution] distribution .
 
 <section class="intro">
 
 The [probability density function][pdf] (PDF) for a [chi][chi-distribution] random variable is
 
 <!-- <equation class="equation" label="eq:chi_pdf" align="center" raw="f(x;\,k) = \frac{2^{{1-k/2}}x^{{k-1}}e^{{-x^{2}/2}}}{\Gamma(k/2)}" alt="Probability density function (PDF) for a chi distribution."> -->
 
 <div class="equation" align="center" data-raw-text="f(x;\,k) = \frac{2^{{1-k/2}}x^{{k-1}}e^{{-x^{2}/2}}}{\Gamma(k/2)}" data-equation="eq:chi_pdf">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/chi/logpdf/docs/img/equation_chi_pdf.svg" alt="Probability density function (PDF) for a chi distribution.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 where `k` is the degrees of freedom and `Γ` denotes the [gamma][gamma-function] function. 
 
 </section>
 
 <!-- /.intro -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var logpdf = require( '@stdlib/stats/base/dists/chi/logpdf' );
 ```
 
 #### logpdf( x, k )
 
 Evaluates the natural logarithm of the [probability density function][pdf] (PDF) for a [chi][chi-distribution] distribution with degrees of freedom `k`.
 
 ```javascript
 var y = logpdf( 0.1, 1.0 );
 // returns ~-0.231
 
 y = logpdf( 0.5, 2.0 );
 // returns ~-0.818
 
 y = logpdf( -1.0, 4.0 );
 // returns -Infinity
 ```
 
 If provided `NaN` as any argument, the function returns `NaN`.
 
 ```javascript
 var y = logpdf( NaN, 1.0 );
 // returns NaN
 
 y = logpdf( 0.0, NaN );
 // returns NaN
 ```
 
 If provided `k < 0`, the function returns `NaN`.
 
 ```javascript
 var y = logpdf( 2.0, -2.0 );
 // returns NaN
 ```
 
 If provided `k = 0`, the function evaluates the natural logarithm of the [PDF][pdf] for a [degenerate distribution][degenerate-distribution] centered at `0`.
 
 ```javascript
 var y = logpdf( 2.0, 0.0 );
 // returns -Infinity
 
 y = logpdf( 0.0, 0.0 );
 // returns Infinity
 ```
 
 #### logpdf.factory( k )
 
 Returns a `function` for evaluating the natural logarithm of the [PDF][pdf] for a [chi][chi-distribution] distribution with degrees of freedom `k`.
 
 ```javascript
 var mylogPDF = logpdf.factory( 6.0 );
 
 var y = mylogPDF( 3.0 );
 // returns ~-1.086
 
 y = mylogPDF( 1.0 );
 // returns ~-2.579
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="examples">
 
 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var randu = require( '@stdlib/random/base/randu' );
 var logpdf = require( '@stdlib/stats/base/dists/chi/logpdf' );
 
 var k;
 var x;
 var y;
 var i;
 
 for ( i = 0; i < 20; i++ ) {
     x = randu() * 10.0;
     k = randu() * 10.0;
     y = logpdf( x, k );
     console.log( 'x: %d, k: %d, ln(f(x;k)): %d', x.toFixed( 4 ), k.toFixed( 4 ), y.toFixed( 4 ) );
 }
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <section class="links">
 
 [chi-distribution]: https://en.wikipedia.org/wiki/Chi_distribution
 
 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
 
 [gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
 
 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function
 
 </section>
 
 <!-- /.links -->