Some Univariate Probability Distributions as Ratios of Others

In probability theory and statistics, functions of random variables play a central role in modeling, simulation, and inference. While the addition and multiplication of random variables are often well understood and frequently applied, the ratio of random variables introduces complex behavior and, in many cases, unexpected distributions. This paper explores some cases in which the ratio (quotient) of two independent univariate random variables yields a new random variable that conforms exactly to a known and named probability distribution.