Probability Density Function

Laplace distribution probability density function (PDF).

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

f left-parenthesis x bar mu comma b right-parenthesis equals StartFraction 1 Over 2 b EndFraction exp left-parenthesis minus StartFraction StartAbsoluteValue x minus mu EndAbsoluteValue Over b EndFraction right-parenthesis

where mu is the location parameter and b > 0 is the scale parameter (also called diversity).

Usage

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

pdf( x, mu, b )

Evaluates the probability density function (PDF) for a Laplace distribution with parameters mu (location parameter) and b > 0 (scale parameter).

var y = pdf( 2.0, 0.0, 1.0 );
// returns ~0.068

y = pdf( -1.0, 2.0, 3.0 );
// returns ~0.061

y = pdf( 2.5, 2.0, 3.0 );
// returns ~0.141

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 b <= 0, the function returns NaN.

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

y = pdf( 2.0, 8.0, 0.0 );
// returns NaN

pdf.factory( mu, b )

Returns a function for evaluating the PDF of a Laplace distribution with parameters mu (location parameter) and b > 0 (scale parameter).

var mypdf = pdf.factory( 10.0, 2.0 );

var y = mypdf( 10.0 );
// returns 0.25

y = mypdf( 5.0 );
// returns ~0.021

y = mypdf( 12.0 );
// returns ~0.092

Examples

var randu = require( '@stdlib/random/base/randu' );
var pdf = require( '@stdlib/math/base/dists/laplace/pdf' );

var mu;
var b;
var x;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    x = randu() * 10.0;
    mu = randu() * 10.0;
    b = randu() * 10.0;
    y = pdf( x, mu, b );
    console.log( 'x: %d, µ: %d, b: %d, f(x;µ,b): %d', x.toFixed( 4 ), mu.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}