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A New Measure of Kurtosis Adjusted for Skewness
Author(s) -
Blest David C.
Publication year - 2003
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00273
Subject(s) - kurtosis , skewness , measure (data warehouse) , mathematics , moment (physics) , asymmetry , range (aeronautics) , statistics , statistical physics , econometrics , computer science , data mining , physics , materials science , classical mechanics , quantum mechanics , composite material
Studies of kurtosis often concentrate on only symmetric distributions. This paper identifies a process through which the standardized measure of kurtosis based on the fourth moment about the mean can be written in terms of two parts: (i) an irreducible component, about L 4 , which can be seen to occur naturally in the analysis of fourth moments; (ii) terms that depend only on moments of lower order, in particular including the effects of asymmetry attached to the third moment about the mean. This separation of the effect of skewness allows definition of an improved measure of kurtosis. This paper calculates and discusses examples of the new measure of kurtosis for a range of standard distributions.