Kurtosis of the logistic-exponential survival distribution

Abstract

In this paper the kurtosis of the logistic-exponential distribution is analyzed. All the moments of this survival distribution are …nite, but do not possess closed-form expressions.The standardized fourth central moment, known as Pearson's coe¢ cient 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, speci…cally 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.