Mean

Gamma distribution expected value.

The expected value for a gamma random variable is

where α > 0 is the shape parameter β > 0 is the rate parameter.

Usage

var mean = require( '@stdlib/stats/base/dists/gamma/mean' );

mean( alpha, beta )

Returns the expected value of a gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

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

v = mean( 4.0, 12.0 );
// returns ~0.333

v = mean( 8.0, 2.0 );
// returns 4.0

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 <= 0, the function returns NaN.

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

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

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var mean = require( '@stdlib/stats/base/dists/gamma/mean' );

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 = mean( alpha, beta );
    console.log( 'α: %d, β: %d, E(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}