Mean

Arcsine distribution expected value.

The expected value for an arcsine random variable is

double-struck upper E left-bracket upper X right-bracket equals 0.5 dot left-parenthesis a plus b right-parenthesis

where a is the minimum support and b is the maximum support.

Usage

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

mean( a, b )

Returns the expected value of an arcsine distribution with parameters a (minimum support) and b (maximum support).

var v = mean( 0.0, 1.0 );
// returns 0.5

v = mean( 4.0, 12.0 );
// returns 8.0

v = mean( 2.0, 8.0 );
// returns 5.0

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 a >= b, the function returns NaN.

var y = mean( 3.0, 2.0 );
// returns NaN

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

Examples

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

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

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