The problem of determining distributions of the product of random variables is one of the most important problems. However, most studies only focus on independence structures on some common distributions of the functions of random variables or stochastic dependence through multivariate normal...

Determining distributions of the functions of random variables is a very important problem with wide applications in Risk Management, Finance, Economics, Science, and many other areas. This paper develops the theory on both density and distribution functions for the quotient Y = X₁/X ₂ and the...

Foster and Hart proposed an operational measure of riskiness for discrete random variables. We show that their defining equation has no solution for many common continuous distributions. We show how to extend consistently the definition of riskiness to continuous random variables. For many...