Some Relationships between the Logistic and the Exponential Distributions

The logistic distribution, known to be similar to the normal distribution, is not known to be well characterized although it has a simple distribution function. In this paper some recent results which relate the logistic and the exponential distributions and mutually characterize both are summarized. A generalization of one of these results in which the logistic is characterized in terms of the functional form of its characteristic function is given.