# Probability Density Function

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.

## Usage

var pdf = require( '@stdlib/math/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/math/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 );
}