Abstract
We establish instability of the characterization of the normal law in Cramer’s theorem with respect to the total variation norm and the entropic distance. Two constructions of counter-examples are provided.
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Keywords
- Independent Random Variable
- Total Variation Distance
- Total Variation Norm
- Arbitrary Probability Distribution
- Entropy Power
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References
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Bobkov, S.G., Chistyakov, G.P., Götze, F. (2012). Chapter 15 Entropic instability of Cramer’s characterization of the normal law. In: van de Geer, S., Wegkamp, M. (eds) Selected Works of Willem van Zwet. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1314-1_15
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