الفهرس 
Basic Notations and TerminologyOnly 14 pages are availabe for public view
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Abstract
The problem of constructing and extending families of probability continuous distributions is one of the important research problems that are still so active in statistics. This is due to several reasons, among them The amount of data available for analysis is growing increasingly faster, requiring new probabilistic distributions to better describe each phenomenon>• the computational and analytical facilities available in programming softwares such as R, Maple and Mathematica can easily tackle the problems involved in computing special functions in these extended distributions• The limitations of the existing distributions and its lack in modeling some stochastic phenomena • The extended families give more flexibility to model various types of data. One of the main objectives of this thesis is to introduce new parametric distributions and investigate its mathematical and statistical properties. The potentiality of the new proposed models is illustrated by means of different real data sets.The thesis consists of five chapters:
In Chapter 1, the role of parameters and a survey for methods of generating continuous univariate distributions are presented. Finally, some definitions and basic concepts which of use through this thesis are shown. In Chapter 2, the exponentiated exponential (EE) distribution is generalized by means of the Marshall-Olkin transformation. It is can be obtained as a compound distribution with mixing exponential model. We verified that the proposed distribution satisfies the geometric extreme stable property. The probability density functions is given, the hazard rate and the mean residual life functions are deduced, the moments are derived and estimates of unknown parameters are obtained. Moreover, an application to a real data set is presented for illustrative purposes. In Chapter 3, We propose a new family of continuous univariate distributions with an extra parameter, the so-called Generalized Poisson Lomax (GPL) distribution, which have the Lomax distribution as submodel. Various structural properties of the new distribution, including the shape behavior of the density and the hazard rate functions, moments, moment generating function and mean residual life, are presented. The strength- stress reliability function R = P(X>Y ) and its estimation are discussed. Also, the estimation of the model parameters is given by maximum likelihood. Simulation studies are carried out to investigate the accuracy of the estimates of the model’s parameters. Finally, we illustrate the importance of the proposed model by means of fitting to two real data sets, one with censored data and the other with complete data. In Chapter 4, A new three parameters continuous distribution which is named the Uniform Truncated Negative Binomial (UTNB) distribution is introduced. It has the Uniform and the Marshall-Olkin Uniform distributions as sub-models. Some reliability and statistical properties of the new distribution are derived, including the shape behavior of the density and hazard rate functions, the mean residual life function, moments and moment generating function, quantiles and related measures. The limiting distributions of the sample extremes, stochastic orderings, entropies and stress-strength reliability are derived. Maximum likelihood estimation is performed. We provide an application of censored data illustrates the potentiality of the proposed distribution. Finally, in chapter 5, the conclusion of the thesis is addressed and further studies on the new distributions may be considered as future work as well as more comparisons with other generalizations of the original distributions can be investigated. The numerical results obtained in this thesis are tabulated whenever possible. These results show that the proposed models can provide a better fit than a recent family of distributions. Comparisons with some other distributions are presented. To the best of our knowledge, we do believe that all the theoretical results stated and proved in this thesis are completely new. The programs used in this thesis are performed on the PC machine, with Intel(R) Core(TM) i5-2450M CPU 2.50 GHz, 4.00 GB of RAM, and the symbolic computation software Mathematica10 has been also used. It is worth mentioning that the new results contained in chapter two are published in“International Journal of Computer Applications. 2015; 121(5).”Also, the new results of chapter three are published in International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 - 29 DEC. 2015 Cairo, Egypt”. Finally, the new results achieved in chapter four are accepted for publication in “Journal of Mathematics and Statistics (2016)”.