Standard Deviation

Inverse gamma distribution standard deviation.

The standard deviation for an inverse gamma random variable with shape parameter α and rate parameter β is

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

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

Usage

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

stdev( alpha, beta )

Returns the standard deviation of a inverse gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var v = stdev( 7.0, 7.0 );
// returns ~0.522

v = stdev( 4.0, 12.0 );
// returns ~2.828

v = stdev( 8.0, 2.0 );
// returns ~0.118

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 <= 2, the function returns NaN.

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

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

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

var v = stdev( 3.0, 0.0 );
// 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/invgamma/stdev' );

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

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + 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 ) );
}