Variance

Discrete uniform distribution variance.

The variance for a discrete uniform random variable is

upper V a r left-parenthesis upper X right-parenthesis equals StartFraction left-parenthesis b minus a plus 1 right-parenthesis squared minus 1 Over 12 EndFraction

where a is the minimum support and b the maximum support of the distribution.

Usage

var variance = require( '@stdlib/math/base/dists/discrete-uniform/variance' );

variance( a, b )

Returns the variance of a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var v = variance( 0, 1 );
// returns ~0.25

v = variance( 4, 12 );
// returns ~6.667

v = variance( -4, 4 );
// returns ~6.667

If a or b is not an integer value, the function returns NaN.

var v = variance( 0.1, 2 );
// returns NaN

v = variance( 0, 2.2 );
// returns NaN

v = variance( NaN, 2 );
// returns NaN

v = variance( 2, NaN );
// returns NaN

If provided a > b, the function returns NaN.

var v = variance( 3, 2 );
// returns NaN

v = variance( -1, -2 );
// returns NaN

Examples

var randint = require( '@stdlib/random/base/discrete-uniform' );
var variance = require( '@stdlib/math/base/dists/discrete-uniform/variance' );

var randa = randint.factory( 0, 10 );
var randb = randint.factory();
var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = randa();
    b = randb( a, a+randa() );
    v = variance( a, b );
    console.log( 'a: %d, b: %d, Var(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}