Mean

Lévy distribution expected value.

The expected value for a Lévy random variable with location μ and scale c > 0 is

double-struck upper E left-bracket upper X right-bracket equals normal infinity

Usage

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

mean( mu, c )

Returns the expected value for a Lévy distribution with location parameter mu and scale parameter c.

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

y = mean( 0.0, 1.0 );
// returns Infinity

y = mean( -1.0, 4.0 );
// returns Infinity

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

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

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

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

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

y = mean( 0.0, -1.0 );
// returns NaN

Examples

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

var mu;
var c;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    mu = ( randu()*10.0 ) - 5.0;
    c = randu() * 20.0;
    y = mean( mu, c );
    console.log( 'µ: %d, c: %d, E(X;µ,c): %d', mu.toFixed( 4 ), c.toFixed( 4 ), y.toFixed( 4 ) );
}