Variance

Student's t distribution variance.

The variance for a Student's t random variable with degrees of freedom ν is

upper V a r left-parenthesis upper X right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column StartFraction nu Over nu minus 2 EndFraction 2nd Column for nu greater-than 2 2nd Row 1st Column normal infinity 2nd Column for 1 less-than nu less-than-or-equal-to 2 EndLayout

For ν smaller than one, the variance is not defined.

Usage

var variance = require( '@stdlib/math/base/dists/t/variance' );

variance( v )

Returns the variance of a Student's t distribution with degrees of freedom v.

var y = variance( 9.0 );
// returns ~1.286

y = variance( 3.5 );
// returns ~2.333

If provided 1 < v <= 2, the function returns infinity.

var y = variance( 1.5 );
// returns Infinity

y = variance( 2.0 );
// returns Infinity

If provided v <= 1, the function returns NaN.

var y = variance( -1.0 );
// returns NaN

y = variance( 0.8 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var variance = require( '@stdlib/math/base/dists/t/variance' );

var v;
var y;
var i;

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