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sidered more exible and e_ective than the uniform distribution. It aims at pro- viding a systematic, detailed study for the properties of Marshall-Olkin extended uniform distribution. For the purpose of the study, the survival function, probability density function and hazard rate function were investigated. These functions were also presented in graphical format and then analyzed. In addition, the mean, variance and other quantiles were studied. The study also discussed the entropy and mixture related to this distribution, besides deriving the limiting distribution of sample extremes. Finally, applications in autoregressive time series modeling were presented as well as many theorems related to the subjects of the study were proved. The _ndings revealed that the Marshall-Olkin extended uniform distribution has many properties, which provides an opportunity for this distribution to be used in many applications. Therefore, scientists, researchers and decision makers should employ these properties in order to be used in new _elds. i Acknowledgements I would like to take this chance to gratefully acknowledge my indebtedness to my supervisor Dr. Raid Salha for his guidance, collaboration, advice, and constant encouragements from the very early stage of this research. I am also grateful to the Faculty of Science at the IUG and all my professors who taught me during my academic journey. Furthermore, my deepest gratitude is also directed to my parents, husband and sons for the support, help, and patience they have shown during the time of studying and preparing this work. Finally, I must o_er special thanks to all those who have participated in making this dream possible, even if it is just one word. iii
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