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Large deviations for some normalized sums of exponentially distributed random variables. (English) Zbl 1265.60025

Summary: We prove large deviation results for sequences of normalized sums which are defined in terms of triangular arrays of exponentially distributed random variables. We also present some examples: one of them might have applications in reliability theory because it concerns the spacings of i.i.d. exponentially distributed random variables; in another one, we consider a sequence of logarithmically weighted means.

MSC:

60F05 Central limit and other weak theorems
60F10 Large deviations
60F15 Strong limit theorems
62G30 Order statistics; empirical distribution functions
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
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