Skewness

Planck (discrete exponential) distribution skewness.

The skewness for a Planck random variable is

normal s times normal k times normal e times normal w left-parenthesis upper X right-parenthesis equals 2 hyperbolic cosine left-parenthesis StartFraction lamda Over 2 EndFraction right-parenthesis

where λ is the shape parameter.

Usage

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

skewness( lambda )

Returns the skewness of a Planck distribution with shape parameter lambda.

var v = skewness( 0.1 );
// returns ~2.0025

v = skewness( 1.5 );
// returns ~2.5894

If provided a shape parameter lambda which is nonpositive or NaN, the function returns NaN.

var v = skewness( NaN );
// returns NaN

v = skewness( -1.5 );
// returns NaN

Examples

var uniform = require( '@stdlib/random/array/uniform' );
var skewness = require( '@stdlib/stats/base/dists/planck/skewness' );

var lambda = uniform( 10, 0.1, 10.0 );

var v;
var i;
for ( i = 0; i < lambda.length; i++ ) {
    v = skewness( lambda[ i ] );
    console.log( 'λ: %d, skew(X;λ): %d', lambda[ i ].toFixed( 4 ), v.toFixed( 4 ) );
}
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