Kurtosis

Lognormal distribution excess kurtosis.

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

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

Installation

npm install @stdlib/stats-base-dists-lognormal-kurtosis

Usage

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

kurtosis( mu, sigma )

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

var y = kurtosis( 2.0, 1.0 );
// returns ~110.936

y = kurtosis( 0.0, 1.0 );
// returns ~110.936

y = kurtosis( -1.0, 4.0 );
// returns 6.235150484159035e+27

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 sigma <= 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-lognormal-kurtosis' );

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

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

C APIs

Usage

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

stdlib_base_dists_lognormal_kurtosis( mu, sigma )

Evaluates the excess kurtosis for a lognormal distribution with location mu and scale sigma.

double out = stdlib_base_dists_lognormal_kurtosis( 0.0, 1.0 );
// returns ~110.936

The function accepts the following arguments:

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

double stdlib_base_dists_lognormal_kurtosis( const double mu, const double sigma );

Examples

#include "stdlib/stats/base/dists/lognormal/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 sigma;
    double mu;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        sigma = random_uniform( 0.1, 5.0 );
        mu = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_lognormal_kurtosis( mu, sigma );
        printf( "µ: %lf, σ: %lf, Kurt(X;µ,σ): %lf\n", mu, sigma, y );
    }
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.