Computational procedures for deriving sampling distributions of attribute-contaminated random variables

Statistical distributions generated from any J- or U-shaped random variables are cumbersome to derive if not completely indefinable and thus are unavailable analytically because of the singularities at the tails of the basic random variable. This paper presents a computational method for providing a numerical convolution derived from a basic U-shaped random variable composed of a continuous part mixed with (or contaminated by) a discrete part at the tails. The J-shaped sampling distribution case is implied as a special case. Though the computations are based on a background Normal Distribution, it can be generalized on any other distribution.Such distributions will open up an area of sampling distributions of mixed random variables that are not elaborately covered in textbooks dealing with the theory of distributions.