Mode

Beta distribution mode.

The mode for a beta random variable is

m o d e left-parenthesis upper X right-parenthesis equals StartFraction alpha minus 1 Over alpha plus beta minus 2 EndFraction

for α > 1 and β > 1. For other values of first shape parameter α and second shape parameter β, the mode is not defined.

Usage

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

mode( alpha, beta )

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

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

v = mode( 4.0, 12.0 );
// returns 0.25

v = mode( 8.0, 2.0 );
// returns 0.8

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

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

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

If provided alpha <= 1, the function returns NaN.

var v = mode( 0.5, 1.0 );
// returns NaN

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

If provided beta <= 1, the function returns NaN.

var v = mode( 1.0, 0.5 );
// returns NaN

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

Examples

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

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

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + 1.0 + EPS;
    beta = ( randu()*10.0 ) + 1.0 + EPS;
    v = mode( alpha, beta );
    console.log( 'α: %d, β: %d, mode(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}