Probability Density Function

Lévy distribution probability density function (PDF).

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

where μ is the location parameter and c > 0 is the scale parameter.

Installation

npm install @stdlib/stats-base-dists-levy-pdf

Usage

var pdf = require( '@stdlib/stats-base-dists-levy-pdf' );

pdf( x, mu, c )

Evaluates the probability density function (PDF) for a Lévy distribution with parameters mu (location parameter) and c (scale parameter).

var y = pdf( 2.0, 0.0, 1.0 );
// returns ~0.11

y = pdf( -1.0, 4.0, 4.0 );
// returns 0.0

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

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

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

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

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

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

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

pdf.factory( mu, c )

Returns a function for evaluating the probability density function (PDF) of a Lévy distribution with parameters mu (location parameter) and c (scale parameter).

var mypdf = pdf.factory( 10.0, 2.0 );

var y = mypdf( 11.0 );
// returns ~0.208

y = mypdf( 20.0 );
// returns ~0.016

Examples

var uniform = require( '@stdlib/random-base-uniform' );
var EPS = require( '@stdlib/constants-float64-eps' );
var pdf = require( '@stdlib/stats-base-dists-levy-pdf' );

var mu;
var c;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    mu = uniform( 0.0, 10.0 );
    x = uniform( mu, mu + 10.0 );
    c = uniform( EPS, 10.0 );
    y = pdf( x, mu, c );
    console.log( 'x: %d, µ: %d, c: %d, f(x;µ,c): %d', x, mu, c, y );
}

C APIs

Usage

#include "stdlib/stats/base/dists/levy/pdf.h"

stdlib_base_dists_levy_pdf( x, mu, c )

Evaluates the probability density for a Lévy distribution with input value x, location parameter mu, and scale parameter c.

double out = stdlib_base_dists_levy_pdf( 2.0, 0.0, 1.0 );
// returns ~0.11

The function accepts the following arguments:

• x: [in] double input value.
• mu: [in] double location parameter.
• c: [in] double scale parameter.

double stdlib_base_dists_levy_pdf( const double x, const double mu, const double c );

Examples

#include "stdlib/stats/base/dists/levy/pdf.h"
#include "stdlib/constants/float64/eps.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 x;
    double c;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        mu = random_uniform( 0.0, 10.0 );
        x = random_uniform( mu, mu + 10.0 );
        c = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
        y = stdlib_base_dists_levy_pdf( x, mu, c );
        printf( "x: %lf, µ: %lf, c: %lf, f(x;µ,c): %lf\n", x, mu, c, 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.