Variance

Weibull distribution variance.

The variance for a Weibull random variable is

where λ > 0 is the shape parameter, k > 0 is the scale parameter, and Γ denotes the gamma function.

Installation

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

Usage

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

variance( k, lambda )

Returns the variance of a Weibull distribution with parameters k (shape parameter) and lambda (scale parameter).

var v = variance( 1.0, 1.0 );
// returns 1.0

v = variance( 4.0, 12.0 );
// returns ~9.311

v = variance( 8.0, 2.0 );
// returns ~0.078

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

var v = variance( NaN, 2.0 );
// returns NaN

v = variance( 2.0, NaN );
// returns NaN

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

var v = variance( 0.0, 1.0 );
// returns NaN

v = variance( -1.0, 1.0 );
// returns NaN

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

var v = variance( 1.0, 0.0 );
// returns NaN

v = variance( 1.0, -1.0 );
// returns NaN

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var variance = require( '@stdlib/stats-base-dists-weibull-variance' );

var opts = {
    'dtype': 'float64'
};
var lambda = uniform( 10, EPS, 10.0, opts );
var k = uniform( 10, EPS, 10.0, opts );

logEachMap( 'k: %0.4f, λ: %0.4f, Var(X;k,λ): %0.4f', k, lambda, variance );

C APIs

Usage

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

stdlib_base_dists_weibull_variance( k, lambda )

Returns the variance of a Weibull distribution with parameters k (shape parameter) and lambda (scale parameter).

double out = stdlib_base_dists_weibull_variance( 4.0, 12.0 );
// returns ~9.311

The function accepts the following arguments:

• k: [in] double shape parameter.
• lambda: [in] double scale parameter.

double stdlib_base_dists_weibull_variance( const double k, const double lambda );

Examples

#include "stdlib/stats/base/dists/weibull/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 lambda;
    double k;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        k = random_uniform( 0.0, 10.0 );
        lambda = random_uniform( 0.0, 10.0 );
        y = stdlib_base_dists_weibull_variance( k, lambda );
        printf( "k: %lf, λ: %lf, Var(X;k,λ): %lf\n", k, lambda, 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.