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About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Logarithm of Probability Density Function

NPM version Build Status Coverage Status

Beta prime distribution logarithm of probability density function (PDF).

The probability density function (PDF) for a beta prime random variable is

$$f(x;\alpha,\beta)= \begin{cases} \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha) + \Gamma(\beta)}{x^{\alpha-1}(1+x)^{-\alpha-\beta}} & \text{ for } x > 0 \\ 0 & \text{ otherwise } \end{cases}$$

where α > 0 is the first shape parameter and β > 0 is the second shape parameter.

Usage

To use in Observable,

logpdf = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-betaprime-logpdf@umd/browser.js' )

To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:

var logpdf = require( 'path/to/vendor/umd/stats-base-dists-betaprime-logpdf/index.js' )

To include the bundle in a webpage,

<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-betaprime-logpdf@umd/browser.js"></script>

If no recognized module system is present, access bundle contents via the global scope:

<script type="text/javascript">
(function () {
    window.logpdf;
})();
</script>

logpdf( x, alpha, beta )

Evaluates the natural logarithm of the probability density function (PDF) for a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var y = logpdf( 0.5, 0.5, 1.0 );
// returns ~-0.955

y = logpdf( 0.1, 1.0, 1.0 );
// returns ~-0.191

y = logpdf( 0.8, 4.0, 2.0 );
// returns ~-1.2

If provided an input value x outside smaller or equal to zero, the function returns -Infinity.

var y = logpdf( -0.1, 1.0, 1.0 );
// returns -Infinity

If provided NaN as any argument, the function returns NaN.

var y = logpdf( NaN, 1.0, 1.0 );
// returns NaN

y = logpdf( 0.0, NaN, 1.0 );
// returns NaN

y = logpdf( 0.0, 1.0, NaN );
// returns NaN

If provided alpha <= 0, the function returns NaN.

var y = logpdf( 0.5, 0.0, 1.0 );
// returns NaN

y = logpdf( 0.5, -1.0, 1.0 );
// returns NaN

If provided beta <= 0, the function returns NaN.

var y = logpdf( 0.5, 1.0, 0.0 );
// returns NaN

y = logpdf( 0.5, 1.0, -1.0 );
// returns NaN

logpdf.factory( alpha, beta )

Returns a function for evaluating the natural logarithm of the PDF for a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var mylogPDF = logpdf.factory( 0.5, 0.5 );

var y = mylogPDF( 0.8 );
// returns ~-1.62

y = mylogPDF( 0.3 );
// returns ~-0.805

Notes

  • 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.

Examples

<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-eps@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-betaprime-logpdf@umd/browser.js"></script>
<script type="text/javascript">
(function () {

var alpha;
var beta;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu();
    alpha = ( randu()*5.0 ) + EPS;
    beta = ( randu()*5.0 ) + EPS;
    y = logpdf( x, alpha, beta );
    console.log( 'x: %d, α: %d, β: %d, ln(f(x;α,β)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}

})();
</script>
</body>
</html>

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.