A Comparative Analysis of Discrete and Continuous Distributions in Risk Assessment Models

Abstract

Risk assessment models often rely on probabilistic frameworks to quantify and manage uncertainty. Choosing an appropriate probability distribution—whether discrete or continuous—is critical to accurately modeling risk in various domains such as finance, engineering, and healthcare. This paper presents a comprehensive comparative analysis of discrete and continuous probability distributions within the context of risk assessment. We examine the statistical properties, modeling flexibility, and computational efficiency of commonly used distributions, including the Binomial, Poisson, Normal, and Exponential distributions. Through simulation studies and real-world case applications, we investigate how the choice of distribution affects risk metrics such as Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR), and expected shortfall. The results highlight scenarios where discrete models are more suitable due to event-based uncertainty, as well as cases where continuous models offer superior accuracy in capturing risk magnitudes. This study provides guidance for practitioners in selecting appropriate distributional frameworks to enhance the reliability and interpretability of risk assessment models.