Preserving Statistic Kendall's Orders

We deal with some properties of Kendall’s statistic Orders. In particular, given two statistic variables we will prove when the order is preserving,not changing anything in the reference aleatory system. It is a rare situation so that we can consider the opposite situation in which some conditionsare changing and the orders might change and not to be always preserved. Then, changing the definition of orders in the statistic initial variables, theimplication could be still true but considering the changing of definition of statistic orders. Instead, even if in this conditions, we analysis wheneverstatistic orders is preserving as well. When initial conditions are more ridge in respect to final results, we will prove why they change the system andthe orders are not preserving.