Standard Deviation

Weibull distribution standard deviation.

The standard deviation for a Weibull random variable is

sigma equals lamda StartRoot normal upper Gamma left-parenthesis 1 plus StartFraction 2 Over k EndFraction right-parenthesis minus left-parenthesis normal upper Gamma left-parenthesis 1 plus StartFraction 1 Over k EndFraction right-parenthesis right-parenthesis squared EndRoot

where λ > 0 is the shape parameter, k > 0 is the scale parameter, and Γ denotes the gamma function.

Usage

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

stdev( k, lambda )

Returns the standard deviation of a Weibull distribution with parameters k (shape parameter) and lambda (scale parameter).

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

v = stdev( 4.0, 12.0 );
// returns ~3.051

v = stdev( 8.0, 2.0 );
// returns ~0.279

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 k <= 0, the function returns NaN.

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

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

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

var 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/weibull/stdev' );

var lambda;
var k;
var v;
var i;

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