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.
where α > 0 is the first shape parameter and β > 0 is the second shape parameter.
Usage
var median = require( '@stdlib/stats/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/float64/eps' );
var median = require( '@stdlib/stats/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 ) );
}