Cumulative Distribution Function

Laplace distribution 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 cdf = require( '@stdlib/math/base/dists/laplace/cdf' );

cdf( x, mu, b )

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

var y = cdf( 2.0, 0.0, 1.0 );
// returns ~0.932

y = cdf( 5.0, 10.0, 3.0 );
// returns ~0.094

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

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

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

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

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

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

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

cdf.factory( mu, b )

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

var mycdf = cdf.factory( 3.0, 1.5 );

var y = mycdf( 1.0 );
// returns ~0.132

y = mycdf( 4.0 );
// returns ~0.743

Examples

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

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 = cdf( 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 ) );
}