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

Wolfgang Kühne; Peter Neumann; Dietrich Stoyan; Helmut Stoyan

Applicationes Mathematicae (1994)

- Volume: 22, Issue: 3, page 331-337
- ISSN: 1233-7234

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topKühne, Wolfgang, et al. "Pairs of successes in Bernoulli trials and a new n-estimator for the binomial distribution." Applicationes Mathematicae 22.3 (1994): 331-337. <http://eudml.org/doc/219099>.

@article{Kühne1994,

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.},

author = {Kühne, Wolfgang, Neumann, Peter, Stoyan, Dietrich, Stoyan, Helmut},

journal = {Applicationes Mathematicae},

keywords = {n-estimator; simulation; silicon wafer; Markov chain; binomial distribution; spatial statistics; -estimator; number of success pairs; Bernoulli trials},

language = {eng},

number = {3},

pages = {331-337},

title = {Pairs of successes in Bernoulli trials and a new n-estimator for the binomial distribution},

url = {http://eudml.org/doc/219099},

volume = {22},

year = {1994},

}

TY - JOUR

AU - Kühne, Wolfgang

AU - Neumann, Peter

AU - Stoyan, Dietrich

AU - Stoyan, Helmut

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

JO - Applicationes Mathematicae

PY - 1994

VL - 22

IS - 3

SP - 331

EP - 337

AB - 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.

LA - eng

KW - n-estimator; simulation; silicon wafer; Markov chain; binomial distribution; spatial statistics; -estimator; number of success pairs; Bernoulli trials

UR - http://eudml.org/doc/219099

ER -

## References

top- [1] J. Besag and P. J. Green, Spatial statistics and Bayesian computation, J. Roy. Statist. Soc. B 55 (1993), 25-37. Zbl0800.62572
- [2] J. Besag, J. C. York and A. Mollié, Bayesian image restauration, with two applications in spatial statistics (with discussion), Ann. Inst. Statist. Math. 43 (1991), 1-59. Zbl0760.62029
- [3] R. J. Carroll and F. Lombard, A note on N estimators for the binomial distribution, J. Amer. Statist. Assoc. 80 (1985), 423-426.
- [4] S. Janson, Runs in m-dependent sequences, Ann. Probab. 12 (1984), 805-818. Zbl0545.60080
- [5] W. Kühne, Some results in subdividing the yield in microelectronic production by measurable parameters (in preparation) (1994)
- [6] I. Olkin, A. J. Petkau and J. V. Zidek, A comparison of n estimators for the binomial distribution, J. Amer. Statist. Assoc. 76 (1981), 637-642. Zbl0472.62037

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