Variance

Beta prime distribution variance.

The variance for a beta prime random variable with first shape parameter α and second shape parameter β is

upper V a r left-parenthesis upper X right-parenthesis equals StartFraction alpha left-parenthesis alpha plus beta minus 1 right-parenthesis Over left-parenthesis beta minus 2 right-parenthesis left-parenthesis beta minus 1 right-parenthesis squared EndFraction

when α > 0 and β > 2. Otherwise, the variance is not defined.

Usage

var variance = require( '@stdlib/math/base/dists/betaprime/variance' );

variance( alpha, beta )

Returns the variance of a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var v = variance( 1.0, 3.0 );
// returns ~0.75

v = variance( 4.0, 12.0 );
// returns ~0.05

v = variance( 8.0, 2.5 );
// returns ~67.556

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 alpha <= 0, the function returns NaN.

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

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

If provided beta <= 2, the function returns NaN.

var v = variance( 1.0, 2.0 );
// returns NaN

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/betaprime/variance' );

var alpha;
var beta;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + 2.0 + EPS;
    v = variance( alpha, beta );
    console.log( 'α: %d, β: %d, Var(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}