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

f left-parenthesis x semicolon mu comma sigma right-parenthesis equals StartFraction 1 Over sigma StartRoot 2 pi EndRoot EndFraction e Superscript minus StartFraction left-parenthesis x minus mu right-parenthesis squared Over 2 sigma squared EndFraction

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

Usage

var logpdf = require( '@stdlib/math/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 randu = require( '@stdlib/random/base/randu' );
var logpdf = require( '@stdlib/math/base/dists/normal/logpdf' );

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 = logpdf( x, mu, sigma );
    console.log( 'x: %d, µ: %d, σ: %d, ln(f(x;µ,σ)): %d', x, mu, sigma, y );
}