Mean

Kumaraswamy's double bounded distribution expected value.

The mean for a Kumaraswamy's double bounded random variable is

double-struck upper E left-bracket upper X right-bracket equals b normal upper Gamma left-parenthesis 1 plus StartFraction 1 Over a EndFraction right-parenthesis normal upper Gamma left-parenthesis b right-parenthesis normal upper Gamma left-parenthesis 1 plus StartFraction 1 Over a EndFraction plus b right-parenthesis

where a is the first shape parameter, b the second shape parameter, and Γ denotes the gamma function.

Usage

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

mean( a, b )

Returns the expected value of a Kumaraswamy's double bounded distribution with first shape parameter a and second shape parameter b.

var v = mean( 1.5, 1.5 );
// returns ~0.512

v = mean( 4.0, 12.0 );
// returns ~0.481

v = mean( 2.0, 8.0 );
// returns 0.3

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 a <= 0, the function returns NaN.

var y = mean( -1.0, 2.0 );
// returns NaN

y = mean( 0.0, 2.0 );
// returns NaN

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

var y = mean( 2.0, -1.0 );
// returns NaN

y = mean( 2.0, 0.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var mean = require( '@stdlib/math/base/dists/kumaraswamy/mean' );

var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = randu() * 10.0;
    b = randu() * 10.0;
    v = mean( a, b );
    console.log( 'a: %d, b: %d, E(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}