According to mathematical and statistical properties of the continuous probability distributions, what is the difference between Log-logistic distribution and Burr XII distribution?
The two distributions are not the same. Except, with some assumptions which is the case in most continuous distributions. Attached here are wikipedia definitions of the Log logistic distribution (Fisk) and Burr XIi distribution.
Log-logistic distribution is a special case of the Burr XII distribution. On the other hand, they both have similar characteristics when it comes to the shapes of the hazard rate functions