AbstractThe one-parameter exponential family is a practically convenient and widely used unified family of distributions, which contains both discrete and continuous distributions that can be used for practical modelling, such as the Binomial, Beta, Normal, etc. The problem of estimating product of means has been explored for independent populations from one-parameter exponential family in a general sense, with a three-stage sampling design proposed and proven to be first-order efficient. The purpose of this paper is to apply the theoretical results to specific applications and to provide practical guidance on implementing the proposed sequential design. One popular application problem of interest is to estimate the system reliability, for which a Beta-Binomial model will be adopted. The other practical problem, which is often encountered in environmental study, is risk assessment and a Normal-Normal model will be used for the case.
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