On the generalized logistic and log-logistic distributions

摘要

In this paper, the generalized logistic and the generalized log-logistic distributions are considered. Some theorems that characterize the generalized logistic distribution are proved. Furthermore, a generalization of the log-logistic distribution is defined and its moments are determined. It is pointed out that the t-approximation for the F-distribution proposed in Ojo (1985) can be used to evaluate the cumulative distribution function of the generalized log-logistic distribution. Finally, some relationships between the generalized log-logistic and other distributions are established.