Mean

Chi distribution expected value.

The expected value for a chi random variable is

double-struck upper E left-bracket upper X right-bracket equals StartRoot 2 EndRoot StartFraction normal upper Gamma left-parenthesis left-parenthesis k plus 1 right-parenthesis slash 2 right-parenthesis Over normal upper Gamma left-parenthesis k slash 2 right-parenthesis EndFraction

where k is the degrees of freedom.

Usage

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

mean( k )

Returns the expected value of a chi distribution with degrees of freedom k.

var v = mean( 9.0 );
// returns ~2.918

v = mean( 0.5 );
// returns ~0.478

If provided k < 0, the function returns NaN.

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

Examples

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

var k;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    k = randu() * 20.0;
    v = mean( k );
    console.log( 'k: %d, E(X,k): %d', k.toFixed( 4 ), v.toFixed( 4 ) );
}