Mean

Beta prime distribution expected value.

The expected value for a beta prime random variable is

double-struck upper E left-bracket upper X right-bracket equals StartFraction alpha Over beta minus 1 EndFraction

where α > 0 is the first shape parameter and β > 1 is the second shape parameter.

Usage

var mean = require( '@stdlib/math/base/dists/betaprime/mean' );

mean( alpha, beta )

Returns the expected value of a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var v = mean( 1.0, 2.0 );
// returns 1.0

v = mean( 4.0, 12.0 );
// returns ~0.364

v = mean( 8.0, 2.0 );
// returns 8.0

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

var v = mean( NaN, 2.0 );
// returns NaN

v = mean( 2.0, NaN );
// returns NaN

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

var v = mean( 0.0, 1.0 );
// returns NaN

v = mean( -1.0, 1.0 );
// returns NaN

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

var v = mean( 1.0, 0.8 );
// returns NaN

v = mean( 1.0, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/math/float64-eps' );
var mean = require( '@stdlib/math/base/dists/betaprime/mean' );

var alpha;
var beta;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + 1.0 + EPS;
    v = mean( alpha, beta );
    console.log( 'α: %d, β: %d, E(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}