Characterizations of Pareto distribution by the properties of neighboring order statistics

It is generally accepted that in the case of the Pareto distribution, the maximum observations far deviate from the smaller ones. In the proposed article, we give the exact meaning to this statement, and also show that the corresponding properties are characteristic for Pareto distributions and similar ones. Some characteristic properties are associated with neighboring ordinal statistics, more precisely, with their relationships, which allows us to obtain results that are independent of the choice of a unit of scale.