Kurtosis

Calculates the kurtosis of a given set of data.

Controller: CodeCogs

Contents

Interface
Kurtosis
Page Comments

Dependents

Interface

C++

Kurtosis

template<class T> doublekurtosis(	int	`n`
	T*	`data`	)

A fundamental task in many statistical analyses is to characterize the location and variability of a data set. A further characterization of the data includes skewness and kurtosis.

Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. That is, data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails.

Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. A uniform distribution would be the extreme case.

The kurtosis for a standard normal distribution is three. For this reason, excess kurtosis is defined as

$\eta_2 =\frac{\sum_{i=1}^n (x_i-\overline{x})^4} {(N-1)\sigma^4}$

(2)

where x is the actual population and $\sigma$ is the standard deviation. This way the standard normal distribution has a kurtosis of zero. Positive kurtosis indicates a peaked distribution and negative kurtosis indicates a flat distribution.

References:

NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm

Example 1

#include <codecogs/statistics/moments/kurtosis.h>
#include <iostream>
 
int main()
{
  float x[5] = {3.4 , 7.1 , 1.5 , 8.6 , 4.9};
  double kurt = Stats::Moments::kurtosis<float>(5, x);
  std::cout << "The population kurtosis is: " << kurt << std::endl;
  return 0;
}

Output:

The population kurtosis is: -0.928457

Parameters

n	the size of the population
data	the actual population data given as an array

Returns

the kurtosis of the given set of data

Authors

Anca Filibiu (August 2005)

Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

Not a member, then Register with CodeCogs. Already a Member, then Login.