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Aim: In statistics, the term sequential analysis refers to a statistical analysis in which the sample size is not fixed in advance. Instead, the inference is made within the course of sampling. Further, sampling is terminated by a predefined stopping rule upon satisfying specific optimality criteria. Inferences may be made much earlier by using sequential procedures than would be possible with classical fixed sample size inference procedures at a much lower cost. Regardless of the type of inference, we seek to make; sequential sampling procedures are derived basically under some optimality criteria.
These optimality criteria could involve minimizing a given loss (cost) function while estimating the unknown parameter(s) by the corresponding sample measures, or constructing a fixed-width confidence interval of a targeted parameter with a predetermined coverage probability, or justifying a given claim regarding the unknown parameter(s) while controlling the Type I and/or Type II error probabilities.
The talk aims to present the most well-known sequential procedures and the customary measures that make the procedure enjoys efficiency, consistency, and others. As an application we use Hall’s three-stage procedure to estimate the inverse coefficient of variation of the normal distribution. We tackle both point and interval estimation. We provide theoretical and Monte Carlo simulation for this study