Variance

F distribution variance.

The variance for a F random variable is

upper V a r left-parenthesis upper X right-parenthesis equals StartFraction 2 d 2 squared left-parenthesis d 1 plus d 2 minus 2 right-parenthesis Over d 1 left-parenthesis d 2 minus 2 right-parenthesis squared left-parenthesis d 2 minus 4 right-parenthesis EndFraction

for d1 > 0 and d2 > 4. Otherwise, the variance is not defined.

Usage

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

variance( d1, d2 )

Returns the variance of a F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

var v = variance( 4.0, 5.0 );
// returns ~9.722

v = variance( 4.0, 12.0 );
// returns ~1.26

v = variance( 8.0, 5.0 );
// returns ~7.639

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

var v = variance( NaN, 5.0 );
// returns NaN

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

If provided d1 <= 0, the function returns NaN.

var v = variance( 1.0, 5.0 );
// returns NaN

v = variance( -1.0, 5.0 );
// returns NaN

If provided d2 <= 4, the function returns NaN.

var v = variance( 3.0, 4.0 );
// 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/f/variance' );

var d1;
var d2;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    d1 = ( randu()*10.0 ) + EPS;
    d2 = ( randu()*20.0 ) + EPS;
    v = variance( d1, d2 );
    console.log( 'd1: %d, d2: %d, Var(X;d1,d2): %d', d1.toFixed( 4 ), d2.toFixed( 4 ), v.toFixed( 4 ) );
}