Abstract
The stability property in Cramér's characterization of the normal law is considered in the case of identically distributed summands. As opposite results, instability is shown with respect to strong distances including the entropic distance to normality (addressing a question of M. Kac).
Original language | English (US) |
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Pages (from-to) | 568-588 |
Number of pages | 21 |
Journal | Theory of Probability and its Applications |
Volume | 57 |
Issue number | 4 |
DOIs | |
State | Published - 2013 |
Keywords
- Cramér's characterization of the normal law
- Cramér's theorem
- Stability problems