Degenerate distribution probability density function (PDF).

Usage no npm install needed!

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  import stdlibStatsBaseDistsDegeneratePdf from 'https://cdn.skypack.dev/@stdlib/stats-base-dists-degenerate-pdf';


Probability Density Function

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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,

Probability density function (PDF) for a degenerate distribution.

where delta is the Dirac delta function.

Dirac delta function.


npm install @stdlib/stats-base-dists-degenerate-pdf


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


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 );


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.






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