Logarithm of Probability Density Function

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

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

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

Installation

npm install @stdlib/stats-base-dists-betaprime-logpdf

Usage

var logpdf = require( '@stdlib/stats-base-dists-betaprime-logpdf' );

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

var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var logpdf = require( '@stdlib/stats-base-dists-betaprime-logpdf' );

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 ) );
}

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.