Skewness

Lognormal distribution skewness.

The skewness for a lognormal random variable with location parameter μ and scale parameter σ > 0 is

s k e w left-parenthesis upper X right-parenthesis equals left-parenthesis exp left-parenthesis sigma squared right-parenthesis plus 2 right-parenthesis StartRoot exp left-parenthesis sigma squared right-parenthesis minus 1 EndRoot

According to the definition, the natural logarithm of a random variable from a lognormal distribution follows a normal distribution.

Usage

var skewness = require( '@stdlib/math/base/dists/lognormal/skewness' );

skewness( mu, sigma )

Returns the skewness for a lognormal distribution with location mu and scale sigma.

var y = skewness( 2.0, 1.0 );
// returns ~6.185

y = skewness( 0.0, 1.0 );
// returns ~6.185

y = skewness( -1.0, 2.0 );
// returns ~414.359

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 sigma <= 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/math/base/dists/lognormal/skewness' );

var sigma;
var mu;
var y;
var i;

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