Mode

Kumaraswamy's double bounded distribution mode.

The mode for a Kumaraswamy's double bounded random variable with first shape parameter a and second shape parameter b is

m o d e left-parenthesis upper X right-parenthesis equals left-parenthesis StartFraction a minus 1 Over a b minus 1 EndFraction right-parenthesis Superscript 1 slash a

for a >= 1, b >=1 and not a = b = 1.

Usage

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

mode( a, b )

Returns the mode of a Kumaraswamy's double bounded distribution with first shape parameter a and second shape parameter b.

var v = mode( 1.5, 1.5 );
// returns ~0.543

v = mode( 4.0, 12.0 );
// returns ~0.503

v = mode( 2.0, 8.0 );
// returns ~0.258

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 a = 1 and b = 1, the function returns NaN.

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

If provided a < 1, the function returns NaN.

var y = mode( -1.0, 2.0 );
// returns NaN

y = mode( 0.0, 2.0 );
// returns NaN

If provided b < 1, the function returns NaN.

var y = mode( 2.0, -1.0 );
// returns NaN

y = mode( 2.0, 0.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var mode = require( '@stdlib/math/base/dists/kumaraswamy/mode' );

var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = randu() * 10.0;
    b = randu() * 10.0;
    v = mode( a, b );
    console.log( 'a: %d, b: %d, mode(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}