Variance
Beta prime distribution variance.
The variance for a beta prime random variable with first shape parameter α
and second shape parameter β
is
when α > 0
and β > 2
. Otherwise, the variance is not defined.
Usage
var variance = require( '@stdlib/stats/base/dists/betaprime/variance' );
variance( alpha, beta )
Returns the variance of a beta prime distribution with parameters alpha
(first shape parameter) and beta
(second shape parameter).
var v = variance( 1.0, 3.0 );
// returns ~0.75
v = variance( 4.0, 12.0 );
// returns ~0.05
v = variance( 8.0, 2.5 );
// returns ~67.556
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 <= 2
, the function returns NaN
.
var v = variance( 1.0, 2.0 );
// returns NaN
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/betaprime/variance' );
var alpha;
var beta;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
alpha = ( randu()*10.0 ) + EPS;
beta = ( randu()*10.0 ) + 2.0 + 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 ) );
}