Kurtosis of the logistic-exponential survival distribution |
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Authors: | Paul J van Staden Robert A R King |
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Institution: | 1. Department of Statistics, University of Pretoria, Pretoria, Gauteng, South Africapaul.vanstaden@up.ac.za;3. Department of Statistics, University of Pretoria, Pretoria, Gauteng, South Africa;4. School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, Australia |
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Abstract: | ABSTRACTIn this article, the kurtosis of the logistic-exponential distribution is analyzed. All the moments of this survival distribution are finite, but do not possess closed-form expressions. The standardized fourth central moment, known as Pearson’s coefficient of kurtosis and often used to describe the kurtosis of a distribution, can thus also not be expressed in closed form for the logistic-exponential distribution. Alternative kurtosis measures are therefore considered, specifically quantile-based measures and the L-kurtosis ratio. It is shown that these kurtosis measures of the logistic-exponential distribution are invariant to the values of the distribution’s single shape parameter and hence skewness invariant. |
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Keywords: | L-moments Quantile function Ratio-of-spread functions Skewness-invariant measure of kurtosis Spread–spread plot |
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