Probability Density Function

Lognormal distribution probability density function (PDF).

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

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

where mu is the location parameter and sigma > 0 is the scale parameter. According to the definition, the natural logarithm of a random variable from a lognormal distribution follows a normal distribution.

Usage

var pdf = require( '@stdlib/math/base/dists/lognormal/pdf' );

pdf( x, mu, sigma )

Evaluates the probability density function (PDF) for a lognormal distribution with parameters mu (location parameter) and sigma (scale parameter).

var y = pdf( 2.0, 0.0, 1.0 );
// returns ~0.157

y = pdf( 1.0, 0.0, 1.0 );
// returns ~0.399

y = pdf( 1.0, 3.0, 1.0 );
// returns ~0.004

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

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

pdf.factory( mu, sigma )

Returns a function for evaluating the probability density function (PDF) of a lognormal distribution with parameters mu (location parameter) and sigma (scale parameter).

var mypdf = factory( 4.0, 2.0 );
var y = mypdf( 10.0 );
// returns ~0.014

y = mypdf( 2.0 );
// returns ~0.025

Examples

var randu = require( '@stdlib/random/base/randu' );
var pdf = require( '@stdlib/math/base/dists/lognormal/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.toFixed( 4 ), mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
}