### Abstract

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.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 20 |

Volume | 2004-84 |

Publication status | Published - 2004 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2004-84 |

### Keywords

- probability theory
- limit theorems

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## Cite this

Mushkudiani, N. A., & Einmahl, J. H. J. (2004).

*Generalized Probability-Probability Plots*. (CentER Discussion Paper; Vol. 2004-84). Econometrics.