Date of Award

Fall 2011

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics


Narayanaswamy Balakrishnan




This thesis investigates nonparametric inference under multiple independent samples with various modes of censoring, and also presents results concerning Pitman Closeness under Progressive Type-II right censoring. For the nonparametric inference with multiple independent samples, the case of Type-II right censoring is first considered. Two extensions to this are then discussed: doubly Type-II censoring, and Progressive Type-II right censoring. We consider confidence intervals for quantiles, prediction intervals for order statistics from a future sample, and tolerance intervals for a population proportion. Benefits of using multiple samples over one sample are discussed. For each of these scenarios, we consider simulation as an alternative to exact calculations. In each case we illustrate the results with data from the literature. Furthermore, we consider two problems concerning Pitman Closeness and Progressive Type-II right censoring. We derive simple explicit formulae for the Pitman Closeness probabilities of the order statistics to population quantiles. Various tables are given to illustrate these results. We then use the Pitman Closeness measure as a criterion for determining the optimal censoring scheme for samples drawn from the exponential distribution. A general result is conjectured, and demonstrated in special cases

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