Kurtosis

Raised cosine distribution excess kurtosis.

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

Installation

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

Usage

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

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

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

C APIs

Usage

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

stdlib_base_dists_cosine_kurtosis( mu, s )

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

double out = stdlib_base_dists_cosine_kurtosis( 0.0, 1.0 );
// returns ~-0.594

The function accepts the following arguments:

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

double stdlib_base_dists_cosine_kurtosis( const double mu, const double s );

Examples

#include "stdlib/stats/base/dists/cosine/kurtosis.h"
#include "stdlib/constants/float64/eps.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 s;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        mu = random_uniform( -50.0, 50.0 );
        s = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
        y = stdlib_base_dists_cosine_kurtosis( mu, s );
        printf( "µ: %lf, s: %lf, Kurt(X;µ,s): %lf\n", mu, s, y );
    }

    return 0;
}

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.