README.md

Cumulative Distribution Function

Laplace distribution cumulative distribution function.

The cumulative distribution function for a Laplace random variable is

$$F(x;\mu,b) =\tfrac{1}{2} + \tfrac{1}{2} \mathop{\mathrm{sgn}}(x-\mu) \left(1-\exp \left(-\frac{|x-\mu|}{b} \right ) \right )$$

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

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 );

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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 );
    }
}