Mode

F distribution mode.

The mode for a F random variable with numerator degrees of freedom d1 and denominator degrees of freedom d2 is

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

for d1 > 2 and d2 > 0. Otherwise, the mode is not defined.

Usage

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

mode( d1, d2 )

Returns the mode of a F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

var v = mode( 4.0, 5.0 );
// returns ~0.357

v = mode( 4.0, 12.0 );
// returns ~0.429

v = mode( 8.0, 4.0 );
// returns 0.5

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

var v = mode( NaN, 3.0 );
// returns NaN

v = mode( 3.0, NaN );
// returns NaN

If provided d1 <= 2, the function returns NaN.

var v = mode( 1.0, 3.0 );
// returns NaN

v = mode( -1.0, 3.0 );
// returns NaN

If provided d2 <= 0, the function returns NaN.

var v = mode( 3.0, 0.0 );
// returns NaN

v = mode( 3.0, -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/f/mode' );

var d1;
var d2;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    d1 = ( randu()*10.0 ) + EPS;
    d2 = ( randu()*10.0 ) + EPS;
    v = mode( d1, d2 );
    console.log( 'd1: %d, d2: %d, mode(X;d1,d2): %d', d1.toFixed( 4 ), d2.toFixed( 4 ), v.toFixed( 4 ) );
}