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Sequential design for comparing two Poisson distributions with delayed observations. (English) Zbl 1137.62051

Summary: Given two Poisson populations with unknown means, it is required to select \(N\) units in three phases. T. Colton [Bull. Inst. Int. Stat. 39, No. 3, 185–200 (1962; Zbl 0113.14004)] assumed that the cost of sampling is equal to the cost of an incorrect choice for half of the sample size. In this paper, Colton’s decision procedure is used to determine a sequential method of sampling when the choice is between two Poisson distributions, the standard performance being determined by the mean. This model is modified by considering delayed observations. This modification leads to major changes in the results. Minimax and maximin approaches are used for determining the optimal position of the boundaries of a sequential experiment.

MSC:

62L05 Sequential statistical design
62C20 Minimax procedures in statistical decision theory

Keywords:

maximin

Citations:

Zbl 0113.14004
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