Standard Deviation

Beta prime distribution standard deviation.

The standard deviation for a beta prime random variable with first shape parameter α and second shape parameter β is

sigma equals StartRoot StartFraction alpha left-parenthesis alpha plus beta minus 1 right-parenthesis Over left-parenthesis beta minus 2 right-parenthesis left-parenthesis beta minus 1 right-parenthesis squared EndFraction EndRoot

when α > 0 and β > 2. Otherwise, the standard deviation is not defined.

Usage

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

stdev( alpha, beta )

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

var v = stdev( 1.0, 3.0 );
// returns ~0.866

v = stdev( 4.0, 12.0 );
// returns ~0.223

v = stdev( 8.0, 2.5 );
// returns ~8.219

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

var v = stdev( NaN, 2.0 );
// returns NaN

v = stdev( 2.0, NaN );
// returns NaN

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

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

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

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

var v = stdev( 1.0, 2.0 );
// returns NaN

v = stdev( 1.0, 0.0 );
// returns NaN

v = stdev( 1.0, -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/betaprime/stdev' );

var alpha;
var beta;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + 2.0 + EPS;
    v = stdev( alpha, beta );
    console.log( 'α: %d, β: %d, SD(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}