Variance

Lévy distribution variance.

The variance for a Lévy random variable with location μ and scale c > 0 is

Installation

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

Usage

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

variance( mu, c )

Returns the variance for a Lévy distribution with location parameter mu and scale parameter c.

var y = variance( 2.0, 1.0 );
// returns Infinity

y = variance( 0.0, 1.0 );
// returns Infinity

y = variance( -1.0, 4.0 );
// returns Infinity

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

var y = variance( NaN, 1.0 );
// returns NaN

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

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

var y = variance( 0.0, 0.0 );
// returns NaN

y = variance( 0.0, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var variance = require( '@stdlib/stats-base-dists-levy-variance' );

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

for ( i = 0; i < 10; i++ ) {
    mu = ( randu()*10.0 ) - 5.0;
    c = randu() * 20.0;
    y = variance( mu, c );
    console.log( 'µ: %d, c: %d, Var(X;µ,c): %d', mu.toFixed( 4 ), c.toFixed( 4 ), y.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_levy_variance( mu, c )

Returns the variance for a Lévy distribution with location mu and scale c.

double out = stdlib_base_dists_levy_variance( 0.0, 1.0 );
// returns Infinity

The function accepts the following arguments:

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

double stdlib_base_dists_levy_variance( const double mu, const double c );

Examples

#include "stdlib/stats/base/dists/levy/variance.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 c;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        mu = random_uniform( -5.0, 5.0 );
        c = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_levy_variance( mu, c );
        printf( "µ: %lf, c: %lf, Var(X;µ,c): %lf\n", 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.