Generalized Probability-Probability Plots

We introduce generalized Probability-Probability (P-P) plots in order to study the one-sample goodness-of-fit problem and the two-sample problem, for real valued data.These plots, that are constructed by indexing with the class of closed intervals, globally preserve the properties of classical P-P plots and are distribution-free under the null hypothesis.We also define the generalized P-P plot process and the corresponding, consistent tests.The behaviour of the tests under contiguous alternatives is studied in detail; in particular, limit theorems for the generalized P-P plot processes are presented.By their structure, the tests perform very well for spike (or pulse) alternatives.We also study the finite sample properties of the tests through a simulation study.