Abstract. The problem of estimating the number, n, of trials, given a sequence of k independent success counts obtained by replicating the n-trial experiment is reconsidered in this paper. In contrast to existing methods it is assumed here that more information than usual is available: not only the numbers of successes are given but also the number of pairs of consecutive successes. This assumption is realistic in a class of problems of spatial statistics. There typically k = 1, in which case the classical estimators cannot be used. The quality of the new estimator is analysed and, for k > 1, compared with that of a classical n-estimator. The theoretical basis for this is the distribution of the number of success pairs in Bernoulli trials, which can be determined by an elementary Markov chain argument.1. Introduction. The standard statistical problem associated with the binomial distribution is that of estimating its probability, p, of success.A much less well studied and considerably harder problem is that of estimating the number, n, of trials. The papers by Olkin, Petkau and Zidek [6] and Carroll and Lombard [3] study this problem for the case where k independent success counts s 1 , . . . , s k are given. Their methods cannot be applied if only one count is considered, k = 1. But just this case appears in some problems of spatial statistics.An important application consists in estimating the fraction of chips on a silicon wafer which are faulty because of technological reasons. In a general setting the spatial problem is as follows. A rectangle is divided into 1991 Mathematics Subject Classification: 62E25, 62F10, 62M30.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.