Modeling mixed type random variables

Mixed type random variables contain both continuous and discrete components, and their role is critical in many well-studied fields. Queuing analysis, stock options, and hydrology rainfall models are among those dependent on mixed random variables to simulate event outcomes. In each of these examples, continuous positive distributions combine with a discrete spike at zero to adequately represent system uncertainty. These problems often require simulation because analytic solutions using these hybrid distributions quickly grow in complexity. Concessions are made, however, when using simulation. In addition to inherent sampling variability, perspective of discrete and continuous components is easily lost when plotting results. This paper details these challenges, and touches on the shifting line between simulations and attainable analytic results. It discusses computational probability's potential to improve model realism and accuracy, introducing MixedAPPL software prototype-an extension of Maplesoft based APPL (A Probability Programming Language)-capable of manipulating mixed type random variables.