Skewness and kurtosis analysis for non-Gaussian distributions

Ahmet Celikoglu and Ugur Tirnakli

Physica A: Statistical Mechanics and its Applications, 2018, vol. 499, issue C, 325-334

Abstract: In this paper we address a number of pitfalls regarding the use of kurtosis as a measure of deviations from the Gaussian. We treat kurtosis in both its standard definition and that which arises in q-statistics, namely q-kurtosis. We have recently shown that the relation proposed by Cristelli et al. (2012) between skewness and kurtosis can only be verified for relatively small data sets, independently of the type of statistics chosen; however it fails for sufficiently large data sets, if the fourth moment of the distribution is finite. For infinite fourth moments, kurtosis is not defined as the size of the data set tends to infinity. For distributions with finite fourth moments, the size, N, of the data set for which the standard kurtosis saturates to a fixed value, depends on the deviation of the original distribution from the Gaussian. Nevertheless, using kurtosis as a criterion for deciding which distribution deviates further from the Gaussian can be misleading for small data sets, even for finite fourth moment distributions. Going over to q-statistics, we find that although the value of q-kurtosis is finite in the range of 0Keywords: Classical statistical mechanics; q-statistics; Systems obeying scaling laws (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:499:y:2018:i:c:p:325-334

DOI: 10.1016/j.physa.2018.02.035

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