Standard Deviation

F distribution standard deviation.

The standard deviation for a F random variable is

sigma equals StartRoot 2 EndRoot StartFraction d 1 Over d 2 minus 2 EndFraction StartRoot StartFraction d 1 plus d 2 minus 2 Over d 1 dot left-parenthesis d 2 minus 4 right-parenthesis EndFraction EndRoot

for d1 > 0 and d2 > 4. Otherwise, the standard deviation is not defined.

Usage

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

stdev( d1, d2 )

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

var v = stdev( 4.0, 5.0 );
// returns ~3.118

v = stdev( 4.0, 12.0 );
// returns ~1.122

v = stdev( 8.0, 5.0 );
// returns ~2.764

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

var v = stdev( NaN, 5.0 );
// returns NaN

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

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

var v = stdev( 1.0, 5.0 );
// returns NaN

v = stdev( -1.0, 5.0 );
// returns NaN

If provided d2 <= 4, the function returns NaN.

var v = stdev( 3.0, 4.0 );
// returns NaN

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

Examples

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

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 = stdev( d1, d2 );
    console.log( 'd1: %d, d2: %d, SD(X;d1,d2): %d', d1.toFixed( 4 ), d2.toFixed( 4 ), v.toFixed( 4 ) );
}