الفهرس 
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Abstract
The aim of this thesis is to introduce a new uni_ed families of polynomials including uni_ed Apostol-Bernoulli, Euler and Genocchi polynomials and derive a connection of them with multivariate discrete distributions and reliability theory. Also, we introduce a new generalization of poly-Cauchy and poly- Bernoulli polynomials and we derive some properties for these polynomials.
The thesis is organized as follows:
Chapter 1: In this chapter, we give a review on some types of important numbers and polynomials such as Stirling numbers, Bernoulli, Euler, Genocchi, Cauchy, poly-Cauchy and poly-Bernoulli. Also, we introduce the reliability concepts for discrete life times.
Chapter 2: This chapter is devoted to investigate two uni_ed families of Apostol-Bernoulli, Euler and Genocchi polynomials. Some properties for these polynomials are derived. Moreover, some relationships between our two polynomials and some types of generalized polynomials are also obtained.
Chapter 3: In this chapter, we give new generalization of poly-Cauchy and poly-Bernoulli numbers and polynomials and derive some identities involving the new numbers and polynomials and some types of Stirling numbers. These give generalization of some relations of poly-Cauchy an poly-Bernoulli numbers and polynomials. Furthermore, we obtain some relations between the multiparameter poly-Cauchy numbers and polynomials and new multipara meter poly-Bernoulli numbers and polynomials.
Chapter 4: In this chapter, we derive a new multivariate discrete distribution which is called multivariate uni_cation of generalized Apostol-Bernoulli, Euler and Genocchi distribution (UABEG). Several properties are studied such as, moments, probability generating function and other properties. Also, we study some properties of this distribution in reliability theory. Maximum likelihood method is used to estimate the parameters and numerical method is used to obtain maximum likelihood estimators (MLEs).