Standard Deviation

Weibull distribution standard deviation.

The standard deviation for a Weibull random variable is

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

Installation

npm install @stdlib/stats-base-dists-weibull-stdev

Usage

var stdev = require( '@stdlib/stats-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-float64-eps' );
var stdev = require( '@stdlib/stats-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 ) );
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.