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Logarithm of Probability Density Function
Evaluate the natural logarithm of the probability density function (PDF) for an inverse gamma distribution.
The probability density function (PDF) for an inverse gamma random variable is
where alpha > 0
is the shape parameter and beta > 0
is the scale parameter.
Installation
npm install @stdlib/stats-base-dists-invgamma-logpdf
Usage
var logpdf = require( '@stdlib/stats-base-dists-invgamma-logpdf' );
logpdf( x, alpha, beta )
Evaluates the natural logarithm of the probability density function (PDF) for an inverse gamma distribution with parameters alpha
(shape parameter) and beta
(rate parameter).
var y = logpdf( 2.0, 0.5, 1.0 );
// returns ~-2.112
y = logpdf( 0.2, 1.0, 1.0 );
// returns ~-1.781
y = logpdf( -1.0, 4.0, 2.0 );
// 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( 2.0, 0.0, 1.0 );
// returns NaN
y = logpdf( 2.0, -0.5, 1.0 );
// returns NaN
If provided beta <= 0
, the function returns NaN
.
var y = logpdf( 2.0, 1.0, 0.0 );
// returns NaN
y = logpdf( 2.0, 1.0, -1.0 );
// returns NaN
logpdf.factory( alpha, beta )
Returns a function
for evaluating the natural logarithm of the PDF for an inverse gamma distribution with parameters alpha
(shape parameter) and beta
(rate parameter).
var mylogPDF = logpdf.factory( 6.0, 7.0 );
var y = mylogPDF( 2.0 );
// returns ~-1.464
Examples
var randu = require( '@stdlib/random-base-randu' );
var logpdf = require( '@stdlib/stats-base-dists-invgamma-logpdf' );
var alpha;
var beta;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
x = randu() * 2.0;
alpha = randu() * 5.0;
beta = randu() * 5.0;
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.