In 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.