# 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.

## Usage

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