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,

Probability density function (PDF) for a degenerate distribution.

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.

JSPM

@stdlib/stats-base-dists-degenerate-logpdf

Package Exports

Readme