Order statistics as minimal sufficient statistics

For some families of probability distributions the form of the minimal sufficient statistic is well known, and some other families are proposed here for which the minimal sufficient statistic is the order statistic. Since it is not possible to find a unique family which includes all the cases where the order statistic is minimal sufficient, a necessary and sufficient condition is given, which characterizes all the situations where this happens, i.e. where no synthesis of the sample information on the parameter is possible without loss of information.