Mean

F distribution expected value.

The expected value for a F random variable with numerator degrees of freedom d1 > 0 and denominator degrees of freedom d2 > 0 is defined as

double-struck upper E left-bracket upper X right-bracket equals StartFraction d 2 Over d 2 minus 2 EndFraction

Usage

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

mean( d1, d2 )

Returns the expected value of a F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

var v = mean( 4.0, 5.0 );
// returns ~1.667

v = mean( 4.0, 12.0 );
// returns ~1.2

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

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

var v = mean( NaN, 3.0 );
// returns NaN

v = mean( 3.0, NaN );
// returns NaN

If provided d1 <= 0, the function returns NaN.

var v = mean( 0.0, 3.0 );
// returns NaN

v = mean( -1.0, 3.0 );
// returns NaN

If provided d2 <= 2, the function returns NaN.

var v = mean( 2.0, 1.8 );
// 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/f/mean' );

var d1;
var d2;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    d1 = ( randu()*10.0 ) + EPS;
    d2 = ( randu()*10.0 ) + EPS;
    v = mean( d1, d2 );
    console.log( 'd1: %d, d2: %d, E(X;d1,d2): %d', d1.toFixed( 4 ), d2.toFixed( 4 ), v.toFixed( 4 ) );
}