Characterization of Distributions by Large Deviation Rates.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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The exponential rate of convergence to zero of large deviation probabilities of the mean of independent and identically distributed random variables is well known. In this note, it is shown that this large deviation rate completely determines the common distribution. This feature becomes noteworthy when contrasted with the fact that the limits of the probabilities of ordinary and moderate deviations of the mean depend very little on the common distribution.
- Statistics and Probability