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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.
npm install @stdlib/stats-base-dists-betaprime-logpdf
var logpdf = require( '@stdlib/stats-base-dists-betaprime-logpdf' );
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
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
- In virtually all cases, using the
logpdf
orlogcdf
functions is preferable to manually computing the logarithm of thepdf
orcdf
, respectively, since the latter is prone to overflow and underflow.
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 ) );
}
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.
See LICENSE.
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