Cumulative Distribution Function

Laplace distribution cumulative distribution function.

The cumulative distribution function for a Laplace random variable is

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

Installation

npm install @stdlib/stats-base-dists-laplace-cdf

Usage

var cdf = require( '@stdlib/stats-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 uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-laplace-cdf' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 100, 0.0, 10.0, opts );
var mu = uniform( 100, 0.0, 10.0, opts );
var b = uniform( 100, 0.0, 10.0, opts );

logEachMap( 'x: %04f, µ: %04f, b: %04f, F(x;µ,b): %04f', x, mu, b, cdf );

C APIs

Usage

#include "stdlib/stats/base/dists/laplace/cdf.h"

stdlib_base_dists_laplace_cdf( x, mu, b )

Evaluates the cumulative distribution function (CDF) for a Laplace distribution with location parameter mu and scale parameter b at a value x.

double out = stdlib_base_dists_laplace_cdf( 2.0, 0.0, 1.0 );
// returns ~0.932

The function accepts the following arguments:

• p: [in] double input value.
• mu: [in] double location parameter.
• b: [in] double rate parameter.

double stdlib_base_dists_laplace_cdf( const double x, const double mu, const double b );

Examples

#include "stdlib/stats/base/dists/laplace/cdf.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double mu;
    double b;
    double x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        mu = random_uniform( -5.0, 5.0 );
        b = random_uniform( 0.0, 20.0 );
        x = random_uniform( 0.0, 1.0 );
        y = stdlib_base_dists_laplace_cdf( x, mu, b );
        printf( "x: %lf, µ: %lf, b: %lf, F(x;µ,b): %lf\n", x, mu, b, y );
    }
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.