Median

Lévy distribution median.

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

upper M e d i a n left-parenthesis upper X right-parenthesis equals mu plus StartFraction c Over 2 left-parenthesis e r f c i n v left-parenthesis 1 slash 2 right-parenthesis right-parenthesis squared EndFraction

Usage

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

median( mu, c )

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

var y = median( 2.0, 1.0 );
// returns ~2.333

y = median( 0.0, 1.0 );
// returns ~0.333

y = median( -2.0, 4.0 );
// returns ~-0.667

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

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

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

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

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

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

Examples

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

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 = median( mu, c );
    console.log( 'µ: %d, c: %d, Median(X;µ,c): %d', mu.toFixed( 4 ), c.toFixed( 4 ), y.toFixed( 4 ) );
}