Generalizations
Several different distributions are sometimes referred to as the generalized log-logistic distribution, as they contain the log-logistic as a special case. These include the Burr Type XII distribution (also known as the Singh-Maddala distribution) and the Dagum distribution, both of which include a second shape parameter. Both are in turn special cases of the even more general generalized beta distribution of the second kind. Another more straightforward generalization of the log-logistic is the shifted log-logistic distribution.
Read more about this topic: Log-logistic Distribution, Related Distributions