### A Fixed Sample Size Selection Procedure Negative Binomial Populations.

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In this paper empirical Bayes methods are applied to construct selection rules for the selection of all good exponential distributions. We modify the selection rule introduced and studied by Gupta and Liang [10] who proved that the regret risk converges to zero with rate $O\left({n}^{-\lambda /2}\right),0<\lambda \le 2$. The aim of this paper is to study the asymptotic behavior of the conditional regret risk ${\mathcal{R}}_{n}$. It is shown that $n{\mathcal{R}}_{n}$ tends in distribution to a linear combination of independent ${\chi}^{2}$-distributed random variables. As an application we...

Voting systems produce an aggregated result of the individual preferences of the voters. In many cases the aggregated collective preference – the result of the voting procedure – mirrors much more than anything else the characteristics of the voting systems. Preferential voting systems work most of the time with equidistant differences between the adjacent preferences of an individual voter. They produce, as voting systems usually do, some paradoxical results under special circumstances. However,...

For a sequence of statistical experiments with a finite parameter set the asymptotic behavior of the maximum risk is studied for the problem of classification into disjoint subsets. The exponential rates of the optimal decision rule is determined and expressed in terms of the normalized limit of moment generating functions of likelihood ratios. Necessary and sufficient conditions for the existence of adaptive classification rules in the sense of Rukhin [Ru1] are given. The results are applied to...

Simon and Weiss (1975) consider the formulation of the clinical trial as a selection procedure (Bechhofer, Kiefer and Sobel, 1968). The object of the trial is to choose the better treatment with probability ≥ P*, where P* is assigned, when the difference in success probabilities is ≥ Δ*, Δ* also being assigned. They consider a family of single step allocation methods for the reduction of the number of patients given the poorer treatment. Using numerical results, Simon and Weiss conclude that if...

There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the eulerian numbers. This result may partially justify a frequent assumption about the equidistribution of random permutations.