The extended slash distribution of the sum of two independent logistic random variables

The concept of extended slash distribution is introduced. For the extended slash distribution of the sum of two independent logistic random variables, the characteristic function, moments, absolute moments and conditional tail expectation are obtained. It is shown that this distribution is related to the logistic and the generalized hyperbolic secant distributions by means of several distributional identities. The log-concavity of the distribution is studied. The self-decomposability of this distribution is also proved. Finally, an asymmetric distribution based on the extended slash distribution of the sum of two independent logistic random variables is introduced. Closed form expressions for the moments and for the conditional tail expectation of this skewed distribution are obtained. This distribution is a fairly flexible model for leptokurtic data as can be seen by fitting it to several datasets.