@stdlib/stats-base-dists-degenerate-logpdf
v0.2.1
Published
Degenerate distribution logarithm of probability density function (logPDF).
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Logarithm of Probability Density Function
Degenerate distribution logarithm of probability density function (logPDF).
Strictly speaking, as a discrete distribution, a degenerate has no probability density function (PDF). Extending the notion of a PDF, we conceptualize the PDF of a degenerate distribution as an infinitely tall spike centered at mu
. More formally,
where delta
is the Dirac delta function.
Installation
npm install @stdlib/stats-base-dists-degenerate-logpdf
Usage
var logpdf = require( '@stdlib/stats-base-dists-degenerate-logpdf' );
logpdf( x, mu )
Evaluates the natural logarithm of the PDF of a degenerate distribution centered at mu
.
var y = logpdf( 2.0, 8.0 );
// returns -Infinity
y = logpdf( 8.0, 8.0 );
// returns Infinity
logpdf.factory( mu )
Returns a function for evaluating the natural logarithm of the PDF of a degenerate distribution centered at mu
.
var mylogpdf = logpdf.factory( 10.0 );
var y = mylogpdf( 10.0 );
// returns Infinity
y = mylogpdf( 5.0 );
// returns -Infinity
y = mylogpdf( 12.0 );
// returns -Infinity
Examples
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var logpdf = require( '@stdlib/stats-base-dists-degenerate-logpdf' );
var mu;
var x;
var y;
var i;
for ( i = 0; i < 100; i++ ) {
x = round( randu()*5.0 );
mu = round( randu()*5.0 );
y = logpdf( x, mu );
console.log( 'x: %d, µ: %d, ln(f(x;µ)): %d', x, mu, y );
}
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.