Logarithm of Probability Density Function

Laplace distribution logarithm of probability density function (PDF).

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

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

Usage

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

logpdf( x, mu, b )

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

var y = logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.693

y = logpdf( -1.0, 2.0, 3.0 );
// returns ~-2.792

y = logpdf( 2.5, 2.0, 3.0 );
// returns ~-1.958

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 b <= 0, the function returns NaN.

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

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

logpdf.factory( mu, b )

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

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

var y = mylogpdf( 10.0 );
// returns ~-1.386

y = mylogpdf( 5.0 );
// returns ~-3.886

y = mylogpdf( 12.0 );
// returns ~-2.386

Notes

In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.

Examples

var randu = require( '@stdlib/random/base/randu' );
var logpdf = require( '@stdlib/stats/base/dists/laplace/logpdf' );

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 = logpdf( x, mu, b );
    console.log( 'x: %d, µ: %d, b: %d, ln(f(x;µ,b)): %d', x.toFixed( 4 ), mu.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}