Skewness

Gumbel distribution skewness.

The skewness for a Gumbel random variable with location μ and scale β is

where ζ is the Riemann zeta function.

Installation

npm install @stdlib/stats-base-dists-gumbel-skewness

Usage

var skewness = require( '@stdlib/stats-base-dists-gumbel-skewness' );

skewness( mu, beta )

Returns the skewness for a Gumbel distribution with location parameter mu and scale parameter beta.

var y = skewness( 2.0, 1.0 );
// returns ~1.14

y = skewness( 0.0, 1.0 );
// returns ~1.14

y = skewness( -1.0, 4.0 );
// returns ~1.14

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

var y = skewness( NaN, 1.0 );
// returns NaN

y = skewness( 0.0, NaN );
// returns NaN

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

var y = skewness( 0.0, 0.0 );
// returns NaN

y = skewness( 0.0, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var skewness = require( '@stdlib/stats-base-dists-gumbel-skewness' );

var beta;
var mu;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    mu = ( randu()*10.0 ) - 5.0;
    beta = randu() * 20.0;
    y = skewness( mu, beta );
    console.log( 'µ: %d, β: %d, skew(X;µ,β): %d', mu.toFixed( 4 ), beta.toFixed( 4 ), y.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.

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License

See LICENSE.

Copyright

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