A Note on a Three-Stage Sequential Confidence Interval for the Mean When the Underlying Distribution Departs Away from Normality
This paper discusses the sensitivity of the normal-based three-stage Hall (Ann. Stat. 9(6):1229–1238, 1981) sequential sampling procedure for estimating the population means to departure from normality. We focus on two estimation problems; The first is to construct a confidence interval for the mean with a prescribed width and coverage probability from two sides; when the explicit form of the distribution is known and the other when the distribution function could be approximated by the first four terms of Edgeworth series. We find the asymptotic characteristics for each confidence interval and discuss their sensitivities as the underlying distribution departs away from normality. The second estimation problem is to test the capability of the constructed intervals to detect possible shifts in the true population mean occurring outside the confidence boundaries. We do so by calculating the characteristic operating functions. For brevity, we present numerical ex-amples with discussions.
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