Mode

Beta prime distribution mode.

The mode for a beta prime random variable is

m o d e left-parenthesis upper X right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column StartFraction alpha minus 1 Over beta plus 1 EndFraction 2nd Column if alpha greater-than-or-equal-to 1 2nd Row 1st Column 0 2nd Column otherwise EndLayout

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

Usage

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

mode( alpha, beta )

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

var v = mode( 8.0, 2.0 );
// returns ~2.333

v = mode( 4.0, 12.0 );
// returns ~0.231

v = mode( 1.0, 2.0 );
// returns 0.0

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 <= 0, the function returns NaN.

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

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

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

var v = mode( 1.0, 0.0 );
// 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/betaprime/mode' );

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 = mode( alpha, beta );
    console.log( 'α: %d, β: %d, mode(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}