Probability Density Function

Degenerate distribution probability density function (PDF).

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 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-pdf

Usage

var pdf = require( '@stdlib/stats-base-dists-degenerate-pdf' );

pdf( x, mu )

Evaluates the PDF of a degenerate distribution centered at mu.

var y = pdf( 2.0, 8.0 );
// returns 0.0

y = pdf( 8.0, 8.0 );
// returns Infinity

pdf.factory( mu )

Returns a function for evaluating the PDF of a degenerate distribution centered at mu.

var mypdf = pdf.factory( 10.0 );

var y = mypdf( 10.0 );
// returns Infinity

y = mypdf( 5.0 );
// returns 0.0

y = mypdf( 12.0 );
// returns 0.0

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var pdf = require( '@stdlib/stats-base-dists-degenerate-pdf' );

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 = pdf( x, mu );
    console.log( 'x: %d, µ: %d, 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.