Pairs of successes in Bernoulli trials and a new n-estimator for the binomial distribution

Volume 22 / 1994

Wolfgang Kühne, Peter Neumann, Dietrich Stoyan, Helmut Stoyan Applicationes Mathematicae 22 (1994), 331-337 DOI: 10.4064/am-22-3-331-337


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.


  • Wolfgang Kühne
  • Peter Neumann
  • Dietrich Stoyan
  • Helmut Stoyan

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