Abstract

Let X be a unimodal continuous random variable with support (?, ?) and Y = min(X, r), ? < r < ?, ? and ? being any real numbers. Then Y is a mixed type random variable, continuous within the range ? < y < r and discrete at Y = r, and we call Y a mixed type of truncated random variable. In this chapter, we derive explicit expressions for the moments of Y for any fixed r and the product moments of arbitrary higher order of the variables X and Y. The results are derived by assuming that the distribution of the random variable is a member of the generalized lambda distribution family. Applications of the results to find the optimal deductibles in the purchase of an automobile insurance policy, and the optimum order size maximizing the expected utility of an investor in an inventory model, are given. The method employed is independent of any specific distributional assumptions, so it can be used for all unimodal continuous distributions.