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.
@article{bwmeta1.element.bwnjournal-article-zmv22z3p331bwm,
author = {Wolfgang K\"uhne and Peter Neumann and Dietrich Stoyan and Helmut Stoyan},
title = {Pairs of successes in Bernoulli trials and a new n-estimator for the binomial distribution},
journal = {Applicationes Mathematicae},
volume = {22},
year = {1994},
pages = {331-337},
zbl = {0812.62027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv22z3p331bwm}
}
Kühne, Wolfgang; Neumann, Peter; Stoyan, Dietrich; Stoyan, Helmut. Pairs of successes in Bernoulli trials and a new n-estimator for the binomial distribution. Applicationes Mathematicae, Tome 22 (1994) pp. 331-337. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv22z3p331bwm/
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