# Kurtosis

Fréchet distribution kurtosis.

The excess kurtosis for a Fréchet random variable shape α > 0, scale s > 0, and location parameter m is

where Γ is the gamma function.

## Usage

var kurtosis = require( '@stdlib/stats/base/dists/frechet/kurtosis' );


#### kurtosis( alpha, s, m )

Returns the excess kurtosis for a Fréchet distribution with shape alpha > 0, scale s > 0, and location parameter m.

var y = kurtosis( 5.0, 1.0, 1.0 );
// returns ~45.092

y = kurtosis( 5.0, 10.0, 1.0 );
// returns ~45.092

y = kurtosis( 5.0, 1.0, 2.0 );
// returns ~45.092


If 0 < alpha <= 4, the function returns +Infinity.

var y = kurtosis( 2.5, 1.0, 1.0 );
// returns Infinity


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

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

y = kurtosis( 1.0, NaN, -2.0 );
// returns NaN

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


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

var y = kurtosis( 0.0, 3.0, 2.0 );
// returns NaN

y = kurtosis( 0.0, -1.0, 2.0 );
// returns NaN


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

var y = kurtosis( 1.0, 0.0, 2.0 );
// returns NaN

y = kurtosis( 1.0, -1.0, 2.0 );
// returns NaN


## Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var kurtosis = require( '@stdlib/stats/base/dists/frechet/kurtosis' );

var alpha;
var m;
var s;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
alpha = ( randu()*20.0 ) + EPS;
s = ( randu()*20.0 ) + EPS;
m = ( randu()*20.0 ) - 40.0;
y = kurtosis( alpha, s, m );
console.log( 'α: %d, s: %d, m: %d, Kurt(X;α,s,m): %d', alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}