Kurtosis

Raised cosine distribution excess kurtosis.

The excess kurtosis for a raised cosine random variable with location parameter mu and scale parameter s is

upper K u r t left-parenthesis upper X right-parenthesis equals StartFraction 6 left-parenthesis 90 minus pi Superscript 4 Baseline right-parenthesis Over 5 left-parenthesis pi squared minus 6 right-parenthesis squared EndFraction

Usage

var kurtosis = require( '@stdlib/math/base/dists/cosine/kurtosis' );

kurtosis( mu, s )

Returns the excess kurtosis for a raised cosine distribution with location parameter mu and scale parameter s.

var y = kurtosis( 2.0, 1.0 );
// returns ~-0.594

y = kurtosis( 0.0, 1.0 );
// returns ~-0.594

y = kurtosis( -1.0, 4.0 );
// returns ~-0.594

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

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

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

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

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

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

Examples

var randu = require( '@stdlib/random/base/randu' );
var kurtosis = require( '@stdlib/math/base/dists/cosine/kurtosis' );

var mu;
var s;
var y;
var i;

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