الفهرس 
Chapter 1: Basic Concepts and DefinitionsOnly 14 pages are availabe for public view
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Abstract
The beta distribution is a continuous probability distribution defined on the interval [0, 1] with two positive shape parameters that appear as exponents of the random variable and control the shape of the distribution. It has been applied to model the behavior of random variables limited to intervals of finite length in a wide variety of disciplines. In Bayesian inference, the beta distribution is the conjugate prior probability distribution for the Bernoulli, binomial and geometric distributions.
Numerous statisticians have developed various forms of this distribution to provide flexible analysis for empirical data. The thesis is devoted to study beta distribution and some composite families of Beta distribution. Moreover, a new mixture of Beta distribution, Inverted Beta Lindley distribution, is derived and studied. The new model will be more flexible than other competing distributions.
The problem of characterizing a distribution is an important problem. Various characterizations have been established in many different directions. An investigator will be vitally interested to know if their model fits the requirements of a particular distribution. characterization of Inverted beta and Inverted Beta Lindley distribution using some method of characterizations is presented.
The thesis has been covered in 4 Chapters described as follows:
Chapter 1 provides some basic definitions and main concepts of reliability distribution that are used throughout the thesis.
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Chapter 2 is devoted to study beta distribution and its statistical properties. The shapes of beta distribution and the estimation problem are also discussed. Applications for beta distribution and some special cases of beta distribution are introduced. Finally, a review of various generalizations of the beta distribution that found in literatures is presented.
Chapter 3 presents a class of generalized beta distributions using composition method and some special cases of it with their properties such as probability density function, hazard function and application. In addition, using mixture method a new three parameter distribution called Inverted Beta Lindley distribution is proposed. The properties and parameter estimation of the new model will be derived and discussed. Moreover, a real data on bladder cancer is used to show that the new model can give consistently a better fit than other models.
Chapter 4 is devoted to discuss some methods of characterization and then some characterizations of the Inverted Beta distribution and the Inverted Beta Lindley distribution will be presented. These characterizations are based on truncated moments and the hazard function.
The Publications of this Thesis are summarized as follows:
1- Kilany, N. M. and Atallah H. M., “Inverted Beta Lindley Distribution” has been published in Journal of Advances in Mathematics, Vol. 13, No. 01, pp. 4074-4085, (2017).
2- Kilany, N. M. and Atallah H. M. “Some characterizations of Inverted Beta and Inverted Beta Lindley Distribution”, submitted for publication in Journal of Statistics Application and Probability.