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 applies 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 uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var pdf = require( '@stdlib/stats-base-dists-normal-pdf' );

var opts = {
    'dtype': 'float64'
};
var sigma = uniform( 10, 0.0, 20.0, opts );
var mu = uniform( 10, -5.0, 5.0, opts );
var x = uniform( 10, 0.0, 10.0, opts );

logEachMap( 'x: %0.4f, µ: %0.4f, σ: %0.4f, f(x;µ,σ): %0.4f', x, mu, sigma, pdf );

C APIs

Usage

#include "stdlib/stats/base/dists/normal/pdf.h"

stdlib_base_dists_normal_pdf( x, mu, sigma )

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

double y = stdlib_base_dists_normal_pdf( 2.0, 0.0, 1.0 );
// returns ~0.054

The function accepts the following arguments:

• x: [in] double input value.
• mu: [in] double mean.
• sigma: [in] double standard deviation.

double stdlib_base_dists_normal_pdf( const double x, const double mu, const double sigma );

Examples

#include "stdlib/stats/base/dists/normal/pdf.h"
#include "stdlib/constants/float64/eps.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double sigma;
    double mu;
    double x;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        x = random_uniform( 0.0, 10.0 );
        mu = random_uniform( -5.0, 5.0 );
        sigma = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
        y = stdlib_base_dists_normal_pdf( x, mu, sigma );
        printf( "x: %lf, µ: %lf, σ: %lf, f(x;µ,σ): %lf\n", 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 © 2016-2026. The Stdlib Authors.