On a Beta-Gamma Discrete Distribution for Thunderstorm Count Modeling with Risk Analysis

Risk management is vital for financial institutions to evaluate and mitigate potential losses. Thunderstorm count modeling with risk analysis is used by various sectors, such as insurance and utility companies, to forecast storm recurrence, analyze risk, and estimate financial losses based on factors like wind speed, hail size, and tornado potential. This paper introduces a novel discrete distribution, the Beta-Gamma Discrete (BGD) distribution, designed for modeling count data that inherently excludes zero values. Developed through the compounding of a discrete gamma distribution with a beta distribution, the BGD offers significant flexibility in handling overdispersion and complex data characteristics. The study derives key statistical properties of the BGD, including its probability mass function, moments, hazard rate function, moment generating function, and mean residual life. A comprehensive characterization theorem is also established. The model’s practical utility is demonstrated through an application to thunderstorm event data from the Kennedy Space Center (KSC), where the frequency of thunderstorms per event is a critical operational concern. The performance of the BGD is thoroughly assessed against established zero-truncated models—namely, the Zero-Truncated Generalized Poisson (ZTGP), Size-Biased Negative Binomial (SBNB), and Zero-Truncated Generalized Negative Binomial (ZTGNB)—using evaluation criteria such as Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Chi-square goodness-of-fit, and the Vuong test. The results consistently show that the BGD provides a superior and more accurate fit for the thunderstorm data, thus help NASA and other space agencies for establishing it as a robust and effective tool for modeling positive count data in meteorological and other applied contexts with risk analysis.