Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability density function (PDF) for a normal distribution.

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-logpdf

Usage

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

logpdf( x, mu, sigma )

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

var y = logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.919

y = logpdf( -1.0, 4.0, 2.0 );
// returns ~-4.737

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

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

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

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

If provided sigma < 0, the function returns NaN.

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

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

var y = logpdf( 2.0, 8.0, 0.0 );
// returns -Infinity

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

logpdf.factory( mu, sigma )

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

var mylogpdf = logpdf.factory( 10.0, 2.0 );

var y = mylogpdf( 10.0 );
// returns ~-1.612

y = mylogpdf( 5.0 );
// returns ~-4.737

Examples

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

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, ln(f(x;µ,σ)): %0.4f', x, mu, sigma, logpdf );

C APIs

Usage

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

stdlib_base_dists_normal_logpdf( x, mu, sigma )

Evaluates the natural logarithm of the probability density function (logPDF) for a normal distribution.

double out = stdlib_base_dists_normal_pdf( 2.0, 0.0, 1.0 );
// returns ~-2.919

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_logpdf( cconst double x, const double mu, const double sigma );

Examples

#include "stdlib/stats/base/dists/normal/logpdf.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( 0.1, 20.0 );
        y = stdlib_base_dists_normal_logpdf( x, mu, sigma );
        printf( "x: %lf, µ: %lf, σ: %lf, ln(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.