Median

Beta distribution median.

The median for a beta random variable is the value for which the regularized incomplete beta function I(α,β) is equal to 0.5, i.e.

upper M e d i a n left-bracket upper X right-bracket equals upper I Subscript one-half Superscript left-bracket negative 1 right-bracket Baseline left-parenthesis alpha comma beta right-parenthesis

where α > 0 is the first shape parameter and β > 0 is the second shape parameter.

Usage

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

median( alpha, beta )

Returns the median of a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var v = median( 1.0, 1.0 );
// returns 0.5

v = median( 4.0, 12.0 );
// returns ~0.239

v = median( 8.0, 2.0 );
// returns ~0.820

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

var v = median( NaN, 2.0 );
// returns NaN

v = median( 2.0, NaN );
// returns NaN

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

var v = median( 0.0, 1.0 );
// returns NaN

v = median( -1.0, 1.0 );
// returns NaN

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

var v = median( 1.0, 0.0 );
// returns NaN

v = median( 1.0, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/math/float64-eps' );
var median = require( '@stdlib/math/base/dists/beta/median' );

var alpha;
var beta;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + EPS;
    v = median( alpha, beta );
    console.log( 'α: %d, β: %d, Median(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}