In goodness-of-fit testing, the goal is to determine if data come from a particular distribution. One graphical approach to test goodness-of-fit is a probability plot. Two probability plots typically used are the probability-probability plot and the quantile-quantile plot, but to use these plots, plotting points are needed. Balakrishnan et al. (2010) proposed a new plotting point based on simultaneous closeness probabilities. This was followed up by a correlation-type goodness-of-fit test based on these plotting points. In this thesis, two tests based on the correlation coefficient test are proposed; in particular, a maximal-correlation coefficient test and a minimal-correlation coefficient test which are based on simultaneous closeness probabilities are developed. Two approaches are considered to investigate these two tests: a grid search method and an averaging method. Numerical results, including illustrative examples, critical values and a power study are also provided.

<p>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</p> / Doctor of Philosophy (PhD)