A note on the ordering of distribution functions of INID random variables

We consider new ordering among continuous distribution functions of independent, but not necessarily identically distributed random variables (INID), and introduce new order statistics defined as the observations from these ordered distribution functions. The new order statistics can be used instead of order statistics from INID random variables, and have the advantage of being independent by construction, unlike the ordinary order statistics. Some examples of ordered distribution functions and graphs are presented and some numerical examples of new order statistics are provided.