Statistical analysis of subdivision schemes in terms of probability distribution

Abstract

The objective of this article is to develop the link between probability distribution theory and subdivision schemes. The distribution theory is a field of statistics and subdivision is a field of Computer Aided Geometric Design, both are independent fields. The analysis of subdivision schemes using probability distribution theory is presented. In our analysis, we explore the important properties such as mean, variance, moments about the origin, moments about mean, measures of skewness and measures of kurtosis of subdivision schemes presented in Chinese Annals of Mathematics, Series B (8(5): 1077-1092, 2017).