Development of statistical convolutions of truncated normal and truncated skew normal distributions with applications

Abstract

ABSTRACTConvolutions of normal random variables often arise in engineering problems, and the probability densities of the sums of these random variables are known in the literature. There are practical situations where specification limits on a process are imposed externally, and the product is typically scrapped if its performance does not fall in the specification range. As such, the actual distribution after inspection is truncated. Despite the practical importance of the role of truncated distributions, there has been little work on the theoretical foundation of convolutions associated with truncated random variables. This is paramount, since convolutions are often used as an important standard in statistical tolerance analysis. In this article, the convolutions of the combinations of truncated normal and truncated skew normal random variables on double and triple truncations are developed. The successful completion of this research task on convolution could help obtain a better understanding of integ...