ComputerAidedGeometricDesign(CAGD)isabranchofcomputationalmathematics. It deals with the mathematical description of shapes for use in different fields. Subdivision is a basic tool to describe smooth curves and surfaces in computer aided geometric design. Since, no single subdivision scheme can be adequate for every situation, so there is always a space to present new subdivision schemes. Initially, subdivision schemes were not suitable for noisy data. So the subdivision schemes based on statistical methods are needed for the refinement of noisy data with outliers. In this thesis, the generalized algorithms for univariate, bivariate stationary and non-stationary subdivision schemes for noisy data with outliers based on regression methods are presented. The comparison with existing subdivision schemes is also presented. The subdivision schemes based on probability distribution by using the relation between Logistic regression and probability distribution are introduced. The schemes generated by the probability distribution have very good properties comparative to the existing subdivision schemes. A new type of analysis of subdivision schemes is presented by using probability distribution theory. The analysis of the families of high arity parametric stationary and non-stationary subdivision schemes is also presented in this thesis. Lane-Riesenfeld algorithm is used in different variant for the generation of binary subdivision schemes. The generalized Lane-Riesenfeld algorithms for the generation of high arity parametric stationary and non-stationary subdivision schemes are also presented.