On δ-record observations: asymptotic rates for the counting process and elements of maximum likelihood estimation

摘要

Given a sequence of random variables {X n ,n≥1} and δ∈?, an observation X n is a δ-record if X n ,…,X n?1}+δ. We obtain, for δ≤0, weak and strong laws of large numbers for the counting process of δ-records among the first n observations from a sequence of independent identically distributed random variables, with common distribution F, possibly discontinuous. We provide examples of our results in the context of common probability distributions. Finally, we show how δ-records can be used for maximum likelihood estimation.