Publications and Preprints

Arnold [1] raised several questions for upper records, including characterizing all limit distributions of normalised partial sums of upper records. We provide some answers in the case when the distribution from which the samples are drawn is bounded above. When the distribution is not bounded above, we give sufficient conditions on the distribution for the properly normalized partial sums to converge to a standard normal distribution. We show that our conditions are general enough so that the examples provided by Arnold are covered by our results.