The assumption that two linear statistics are identically distributed can be used to characterize various populations. According to B. Ramachandran and C.R. Rao theorem, if under the additional conditions the two sample means (X1, ..., Xn1)/n1 and (X1, ..., Xn2)/n2 have the same distribution as the monomial X1 then this monomial has a Cauchy law. The stability estimation in this theorem is investigated in our paper.
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