Skewness

F distribution skewness.

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

s k e w left-parenthesis upper X right-parenthesis equals StartFraction left-parenthesis 2 d 1 plus d 2 minus 2 right-parenthesis StartRoot 8 left-parenthesis d 2 minus 4 right-parenthesis EndRoot Over left-parenthesis d 2 minus 6 right-parenthesis StartRoot d 1 left-parenthesis d 1 plus d 2 minus 2 right-parenthesis EndRoot EndFraction

for d1 > 0 and d2 > 6. Otherwise, the skewness is not defined.

Usage

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

skewness( d1, d2 )

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

var v = skewness( 4.0, 7.0 );
// returns ~10.614

v = skewness( 4.0, 12.0 );
// returns ~3.207

v = skewness( 8.0, 7.0 );
// returns ~10.088

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

var v = skewness( NaN, 7.0 );
// returns NaN

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

If provided d1 <= 0, the function returns NaN.

var v = skewness( 1.0, 7.0 );
// returns NaN

v = skewness( -1.0, 7.0 );
// returns NaN

If provided d2 <= 6, the function returns NaN.

var v = skewness( 3.0, 6.0 );
// returns NaN

v = skewness( 3.0, 5.5 );
// returns NaN

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

Examples

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

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

for ( i = 0; i < 10; i++ ) {
    d1 = ( randu()*10.0 ) + EPS;
    d2 = ( randu()*20.0 ) + EPS;
    v = skewness( d1, d2 );
    console.log( 'd1: %d, d2: %d, skew(X;d1,d2): %d', d1.toFixed( 4 ), d2.toFixed( 4 ), v.toFixed( 4 ) );
}