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A New Measure of Kurtosis Adjusted for Skewness

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  • David C. Blest

Abstract

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.

Suggested Citation

  • David C. Blest, 2003. "A New Measure of Kurtosis Adjusted for Skewness," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(2), pages 175-179, June.
    • Handle: RePEc:bla:anzsta:v:45:y:2003:i:2:p:175-179
    DOI: 10.1111/1467-842X.00273
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    Cited by:

    1. Claudio Giovanni Borroni & Lucio De Capitani, 2022. "Some measures of kurtosis and their inference on large datasets," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 573-607, December.
    2. Rosaria Simone, 2022. "On finite mixtures of Discretized Beta model for ordered responses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 828-855, September.
    3. Dragan Đorić & Emilija Nikolić-Đorić & Vesna Jevremović & Jovan Mališić, 2009. "On measuring skewness and kurtosis," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(3), pages 481-493, May.
    4. Izquierdo, Alejandro & Llopis, Jimena & Muratori, Umberto & Ruiz, José Juan, 2016. "In Search of Larger Per Capita Incomes: How To Prioritize across Productivity Determinants?," IDB Publications (Working Papers) 7511, Inter-American Development Bank.

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