Statistical properties of gilbert's burst noise model

Abstract

Simple statistical procedures for analyzing error data, e.g., in digital data transmission systems, are usually based on the assumption of independence. This paper studies the performance and potential utility of such simple statistical procedures in the case of nonindependent error occurrences. The burst noise model is selected for this purpose because of its neatness, its mathematical tractability, its built-in structure of dependence, and its importance in communication theory. We show that statistical procedures designed under the assumption of independence tend to be conservative for the burst noise model. For example, the usual binomial test will reject, on the average, more channels with small error rates than it would if the errors were independent. The case that the sample size n and the error rate ρ converge in such a way that nρ→ µ 0 is also studied. It is shown that the error process can be approximated by a compound Poisson process in continuous time t. The statistical implications of this fact are also discussed.