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| 概要 |
We shall consider the problem to decide between two hypotheses concerning the unknown population parameter when our population is distributed in one parameter exponential distribution, under the follo...wing set up of sampling. A sample of prescribed size $ m $ is decided to be drawm from our population, and moreover we (A) may or (B) may not draw a second independent sample of another prescribed size $ n $ from the same population. This last choice decision between two alternatives (A) and (B) is assumed to be made in view of the risk defined in terms of the expected loss due to the error with reference to a given Bayesian distribution of the population parameter and the costs due to samplings and observations. It is noted that somewhat similar but not identical problem was discussed by Anderson [1] for normal distributions. The purpose of our paper is to show that the notion of additive family of sufficient statistics is useful in getting concrete results through the comparisons of the risks associated two alternatives. We shall be concerned with the following two cases when the continuous distribution is distributed (I) over all real line, and (II) over all positive part of it.続きを見る
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