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On large deviations and density functions

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Abstract

Suppose thatX1,X2, ... is a sequence of absolutely continuous or integer valued random variables with corresponding probability density functionsfn(x). Let {φn} ∞ n=1 be a sequence of real numbers, then necessary and sufficient conditions are given forn−1 logfn(φn)-n−1 log P (Xn>φn)=0(1) asn→∞.

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References

  1. Killeen, T., Hettmansperger, T. and Sievers, G. (1972). An elementary theorem on the probability of large deviations,Ann. Math. Statist.,43, 181–192.

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  1. The University of Connecticut, Connecticut, USA

    Timothy J. Killeen

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  1. Timothy J. Killeen
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Killeen, T.J. On large deviations and density functions. Ann Inst Stat Math 31, 315–317 (1979). https://doi.org/10.1007/BF02480288

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  • DOI: https://doi.org/10.1007/BF02480288

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