Abstract
The paper considers some properties of measures of asymmetry and peakedness of one dimensional distributions. It points to some misconceptions of the first and the second Pearson coefficients, the measures of asymetry and shape, that frequently occur in introductory textbooks. Also it presents different ways for obtaining the estimated values for the coefficients of skewness and kurtosis and statistical tests which include them.
Similar content being viewed by others
References
Blest D.C. (2003). A new measure of kurtosis adjusted for skewness. Aust. N. Z. J. Stat. 45: 175–179
Byers, R.H.: On the maximum of the standardized fourth moment. Working paper (2000)
Cramer H. (1957). Mathematical Methods of Statistics. Princeton University Press, Seventh Printing, Princeton
D’Agostino R.B., Belanger A. and D’Agostino R.B. (1990). A suggestion for using powerful and informative tests of normality. Am. Stat. 44: 316–321
Darlington R.B. (1970). Is kurtosis really ‘peakedness’. Am. Stat. 24: 19–22
De Carlo L.T. (1997). On the meaning and use of kurtosis. Psychol. Methods 2: 292–307
Dyson F.J. (1943). A note on kurtosis. J. R. Stat. Soc. 106: 360–361
Fisher R.A. (1930). The moments of the distribution for normal samples of measures of departures from normality. Proc. R. Soc. London, Series A 130: 16–28
Geary R.C. (1947). Testing for normality. Biometrika 34: 209–242
Gosset W.S. (1927). “Student” Errors of Routine Analysis. Biometrika 19: 151–164
Hopkins K.D. and Weeks D.L. (1990). Tests for normality and measures of skewness and kurtosis: their place in research reporting. Educ. Psychol. Measure. 50: 717–729
Jarque C.M. and Bera A.K. (1987). A test for normality of observations and regression residuals. Int. Stat. Rev. 55: 163–172
Kaplansky I. (1945). A common error concerning kurtosis. J. Am. Stat. Assoc. 40: 259
Kendall M.G. and Stuart A. (1958). The Advanced Theory of Statistics, vol. 1. Charles Griffin, London
Pearson K. (1895). Contribution to the mathematical theory of evolution, II: Skew variation in homogenous material. Philos. Trans. R. Soc. London 186: 343–414
Pearson E.S. and Hartley H.O. (1958). Biometrika Tables for Statisticians, vol. 1. Cambridge University Press, Cambridge
Stoyanov J.M. (1987). Counterexamples in Probability. John Wiley & Sons, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Đorić, D., Nikolić-Đorić, E., Jevremović, V. et al. On measuring skewness and kurtosis. Qual Quant 43, 481–493 (2009). https://doi.org/10.1007/s11135-007-9128-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11135-007-9128-9