A new measure of kurtosis adjusted for skewness

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 L4, 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.