README.md

Kurtosis

Laplace distribution excess kurtosis.

The excess kurtosis for a Laplace random variable with location parameter mu and scale parameter b > 0 is

$$\mathop{\mathrm{Kurt}}\left( X \right) = 3$$

Usage

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

kurtosis( mu, b )

Returns the excess kurtosis for a Laplace distribution with location parameter mu and scale parameter b.

var y = kurtosis( 2.0, 1.0 );
// returns 3.0

y = kurtosis( 0.0, 1.0 );
// returns 3.0

y = kurtosis( -1.0, 4.0 );
// returns 3.0

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 b <= 0, the function returns NaN.

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

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

Examples

var uniform = require( '@stdlib/random/array/uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var kurtosis = require( '@stdlib/stats/base/dists/laplace/kurtosis' );

var opts = {
    'dtype': 'float64'
};
var mu = uniform( 10, -5.0, 5.0, opts );
var b = uniform( 10, 0.0, 20.0, opts );

logEachMap( 'µ: %0.4f, b: %0.4f, Kurt(X;µ,b): %0.4f', mu, b, kurtosis );

---

C APIs

Usage

#include "stdlib/stats/base/dists/laplace/kurtosis.h"

stdlib_base_dists_laplace_kurtosis( mu, b )

Evaluates the excess kurtosis for a Laplace distribution with location parameter mu and scale parameter b.

double out = stdlib_base_dists_laplace_kurtosis( 0.0, 1.0 );
// returns 3.0

The function accepts the following arguments:

• mu: [in] double location parameter.
• b: [in] double scale parameter.

double stdlib_base_dists_laplace_kurtosis( const double mu, const double b );

Examples

#include "stdlib/stats/base/dists/laplace/kurtosis.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double mu;
    double b;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        mu = random_uniform( -5.0, 5.0 );
        b = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_laplace_kurtosis( mu, b );
        printf( "µ: %lf, b: %lf, Kurt(X;µ,b): %lf\n", mu, b, y );
    }
}