A numerical algorithm for computing exact distribution of a truncated random variable when truncation points are assigned point masses
When continuous random variables are truncated at one or two points and point mass assigned to the truncation points, the distribution of the average of the random variables may not have an analytical form. This article presents an algorithm for computing exact percentiles of the sampling distribution of averages of small numbers of independent, truncated random variables. This methodology may be applicable to cases where there is a mixture of a continuous random variable with discrete part at one or both end points. Applications can be in areas of reliability and survival analysis where censoring is widely used; however, we were looking at using this method in new quality control schemes, whereby an item in batch or lot may be evaluated as defective, marginal or effective. Although the defective and effective can assume values of 0 and 1, respectively, the marginal part may be a continuous random variable assuming values between 0 and 1. 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 sampling distributions.
transformation convolution j-shaped random variables tolerance level contaminated continuous-discrete distribution domain compression collapsing of probability cells