Variance

Inverse gamma distribution variance.

The variance for an inverse gamma random variable with shape parameter α and rate parameter β is

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

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

Usage

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

variance( alpha, beta )

Returns the variance of a inverse gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var v = variance( 7.0, 7.0 );
// returns ~0.272

v = variance( 4.0, 12.0 );
// returns 8.0

v = variance( 8.0, 2.0 );
// returns ~0.014

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 <= 2, the function returns NaN.

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

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

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

var v = variance( 3.0, 0.0 );
// returns NaN

v = variance( 3.0, -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/invgamma/variance' );

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

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + 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 ) );
}