M.Sc.

        In this thesis, we consider the extreme value distn. of two parameters for the reason of its appearance in many statistical fields of applications. Mathematical and statistical properties of the distn. such as moments and higher moments are collected and unified and the properties of reliability and hazard functions of the distn.are illustrated.The chi-square goodness - of - fit is used to test whether the generated samples from the standardized extreme value distn. by Monte Carlo simulation are acceptable for use.These samples are used to estimate the distn.

The main objective of this thesis is to introduce fractional integro-differential equations using a modified type of operators, which consists of the same order fractional differentiation and fractional integration. Also,

The aim of this thesis is studying some numerical methods for solving Stochastic Differential Equation. The mathematical preliminary required to understand these numerical methods is proposed. Since many stochastic differential equations do not have explicit solution, Euler-Maruyama and Milstein numerical methods are used. The numerical simulation for different selected examples are implemented. The necessary concluding remarks are provided.