It is generally accepted that in the case of the Pareto distribution, maximal observations far deviate from smaller ones. In the proposed article, we give the exact meaning to this statement and also show that the corresponding properties are characteristic for the 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 which are independent of the choice of the unit of the scale.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 486, 2019, pp. 63–70.
Translated by S. Yu. Pilyugin.
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Volchenkova, I.V., Klebanov, L.B. Characterization of the Pareto Distribution by Properties of Neighboring Order Statistics. J Math Sci 258, 777–781 (2021). https://doi.org/10.1007/s10958-021-05580-3