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

• Autorzy: Wolfgang Kühne , Peter Neumann , Dietrich Stoyan , Helmut Stoyan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

n-estimator; simulation; silicon wafer; Markov chain; binomial distribution

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1993-1995
• Tom: 22
• Numer: 3
• Strony: 331-337

Daty

wydano

1994

otrzymano

1993-06-08

Twórcy

autor

Wolfgang Kühne

• Beilstr. 11, 01277 Dresden, Germany

autor

Peter Neumann

• Technische Universität Dresden, Fachbereich Mathematik, 01062 Dresden, Germany

autor

Dietrich Stoyan

• Tu Bergakademie Freiberg, Fachbereich Mathematik, 09596 Freiberg, Germany

autor

Helmut Stoyan

• Tu Bergakademie Freiberg, Fachbereich Mathematik, 09596 Freiberg, Germany

Bibliografia

• [1] J. Besag and P. J. Green, Spatial statistics and Bayesian computation, J. Roy. Statist. Soc. B 55 (1993), 25-37.
• [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.
• [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.
• [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.