Probability Density Function

Normal distribution probability density function (PDF).

The probability density function (PDF) for a normal random variable is

where µ is the mean and σ is the standard deviation.

Installation

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

Usage

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

pdf( x, mu, sigma )

Evaluates the probability density function (PDF) for a normal distribution with parameters mu (mean) and sigma (standard deviation).

var y = pdf( 2.0, 0.0, 1.0 );
// returns ~0.054

y = pdf( -1.0, 4.0, 2.0 );
// returns ~0.009

If provided NaN as any argument, the function returns NaN.

var y = pdf( NaN, 0.0, 1.0 );
// returns NaN

y = pdf( 0.0, NaN, 1.0 );
// returns NaN

y = pdf( 0.0, 0.0, NaN );
// returns NaN

If provided sigma < 0, the function returns NaN.

var y = pdf( 2.0, 0.0, -1.0 );
// returns NaN

If provided sigma = 0, the function evaluates the PDF of a degenerate distribution centered at mu.

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

y = pdf( 8.0, 8.0, 0.0 );
// returns Infinity

pdf.factory( mu, sigma )

Partially apply mu and sigma to create a reusable function for evaluating the PDF.

var mypdf = pdf.factory( 10.0, 2.0 );

var y = mypdf( 10.0 );
// returns ~0.199

y = mypdf( 5.0 );
// returns ~0.009

Examples

var randu = require( '@stdlib/random-base-randu' );
var pdf = require( '@stdlib/stats-base-dists-normal-pdf' );

var sigma;
var mu;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    mu = (randu() * 10.0) - 5.0;
    sigma = randu() * 20.0;
    y = pdf( x, mu, sigma );
    console.log( 'x: %d, µ: %d, σ: %d, f(x;µ,σ): %d', x, mu, sigma, 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.