Approximations of δ -record probabilities in i.i.d. and trend models

Abstract

We study the probability of occurrence of -records in a model with linear trend. While this probability has been studied in the iid case, the existence of a trend makes its analysis much more involved. Asymptotic properties of this probability have been studied in the literature when the number of observations is large. However, no approximations are known when the number of observations is small. We propose a first order approximation as a function of both the values of and the trend. We assess our results via Montecarlo simulations finding that the approximations are accurate for a small-moderate number of observations.