Contributions to sequential analysis
This thesis will consider two problems in sequential analysis. A new two-stage sampling methodology is explored for the minimum risk point estimation of the range in a power family distribution. This modification of Ghosh et al.'s (1983) two-stage estimation technique is proposed along the lines of Mukhopadhyay and Duggan (1997, 1999) by assuming a prior knowledge of a positive lower bound for the otherwise unknown range parameter. Expressions for the risk associated with the conventional sample maximum order statistic as well as another new estimator are investigated. Various second-order asymptotic analyses are supplemented by interesting exact and simulation results. The second problem is concerned with point estimation of the scale parameter in an exponential distribution following a sequential sampling scheme. The performances of both biased and bias-corrected estimators based on the sample mean and the randomly stopped sample size are investigated via simulation. We then address the estimation problems for the reliability parameter, that is the probability of an observation surviving beyond a particular point t in the one-sample. We investigate "invariance (of MLE) based" estimators as well as estimators based upon the bias-corrected reliability function developed in Mukhopadhyay et al. (1997). The merits of these estimators are examined through simulation. These ideas are subsequently extended to the two-sample problem. Here the goal is to estimate that how many times more likely is it for an observation from one exponentially distributed population to survive beyond time point t, compared with another population. Twelve estimators will be developed and compared towards this end.
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