Variance

Weibull distribution variance.

The variance for a Weibull random variable is

upper V a r left-parenthesis upper X right-parenthesis equals lamda squared left-bracket normal upper Gamma left-parenthesis 1 plus StartFraction 2 Over k EndFraction right-parenthesis minus left-parenthesis normal upper Gamma left-parenthesis 1 plus StartFraction 1 Over k EndFraction right-parenthesis right-parenthesis squared right-bracket

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

Usage

var variance = require( '@stdlib/math/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 randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/math/float64-eps' );
var variance = require( '@stdlib/math/base/dists/weibull/variance' );

var lambda;
var k;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    k = ( randu()*10.0 ) + EPS;
    lambda = ( randu()*10.0 ) + EPS;
    v = variance( k, lambda );
    console.log( 'k: %d, λ: %d, Var(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) );
}