Logarithm of Cumulative Distribution Function

Laplace distribution logarithm of cumulative distribution function.

The cumulative distribution function for a Laplace random variable is

upper F left-parenthesis x semicolon mu comma b right-parenthesis equals one-half plus one-half s g n left-parenthesis x minus mu right-parenthesis left-parenthesis 1 minus exp left-parenthesis minus StartFraction StartAbsoluteValue x minus mu EndAbsoluteValue Over b EndFraction right-parenthesis right-parenthesis

where mu is the location parameter and b > 0 is the scale parameter.

Usage

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

logcdf( x, mu, b )

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

var y = logcdf( 2.0, 0.0, 1.0 );
// returns ~-0.07

y = logcdf( 5.0, 10.0, 3.0 );
// returns ~-2.364

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

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

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

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

If provided b <= 0, the function returns NaN.

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

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

logcdf.factory( mu, b )

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

var mylogcdf = logcdf.factory( 3.0, 1.5 );

var y = mylogcdf( 1.0 );
// returns ~-2.025

y = mylogcdf( 4.0 );
// returns ~-0.297

Examples

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

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 = logcdf( 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 ) );
}