Standard Deviation

Arcsine distribution standard deviation.

The standard deviation for an arcsine random variable with minimum support a and maximum support b is

sigma equals StartFraction 1 Over StartRoot 8 EndRoot EndFraction left-parenthesis b minus a right-parenthesis

Usage

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

stdev( a, b )

Returns the standard deviation of an arcsine distribution with parameters a (minimum support) and b (maximum support).

var v = stdev( 0.0, 1.0 );
// returns ~0.125

v = stdev( 4.0, 12.0 );
// returns 8.0

v = stdev( 2.0, 8.0 );
// returns ~4.5

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 a >= b, the function returns NaN.

var v = stdev( 3.0, 2.0 );
// returns NaN

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

Examples

var randu = require( '@stdlib/random/base/randu' );
var stdev = require( '@stdlib/math/base/dists/arcsine/stdev' );

var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = ( randu()*10.0 );
    b = ( randu()*10.0 ) + a;
    v = stdev( a, b );
    console.log( 'a: %d, b: %d, SD(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}