Variance
The variance for a beta random variable is
where α > 0 is the first shape parameter and β > 0 is the second shape parameter.
Usage
var variance = require( '@stdlib/stats/base/dists/beta/variance' );
variance( alpha, beta )
Returns the variance of a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).
var v = variance( 1.0, 1.0 );
// returns ~0.083
v = variance( 4.0, 12.0 );
// returns ~0.011
v = variance( 8.0, 2.0 );
// returns ~0.015
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 <= 0, the function returns NaN.
var 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/float64/eps' );
var variance = require( '@stdlib/stats/base/dists/beta/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 ) );
}