Asymptotic results for sums and extremes

Rita Giuliano, Claudio Macci, Barbara Pacchiarotti

Published 2022-10-05Version 1

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant, and a weak convergence to a centered Gaussian distribution (when such random variables are properly centered and rescaled). We talk about non-central moderate deviations when the weak convergence is towards some non-Gaussian weak limit. In this paper we prove a non-central moderate deviation result for the bivariate sequence of sums and maxima of i.i.d. random variables. Moreover, we prove a moderate deviation result for sums of partial minima of i.i.d. exponential random variables.