# @stdlib/stats-base-dists-degenerate-pdf

0.2.2 • Public • Published

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# 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,

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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.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-degenerate-pdf`

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