Stability of a characterization by the identical distribution of linear forms
Romanas Yanushkevichius, Olga Yanushkevichiene · Statistics · 2007
The assumption that two linear statistics are identically distributed can be used to characterize various populations. This is an object of the so-called characterization theorems. But if the assumptions of the characterization theorem are fulfilled only approximately, then may we state that the conclusion of this characterization is also fulfilled approximately? Theorems, in which this kind of problems are considered, are called the stability theorems. According to Eaton's theorem, if under the additional conditions, the two linear statistics and have the same distribution as the monomial X 1, then this monomial has a symmetric stable distribution of order α. The stability estimation in this theorem is investigated in the paper.