Abstract:
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.
