Modeling the inter-arrival time between severe storms in the United States using finite mixtures

When inter-arrival times between events follow an exponential distribution, this implies a Poisson frequency of events, as both models assume events occur independently and at a constant average rate. However, these assumptions are often violated in real-insurance applications. When the rate at which events occur changes over time, the exponential distribution becomes unsuitable. In this paper, we study the distribution of inter-arrival times of severe storms, which exhibit substantial variability, violating the assumption of a constant average rate. A new approach is proposed for modeling severe storm recurrence patterns using a finite mixture of log-normal distributions. This approach effectively captures both frequent, closely spaced storm events and extended quiet periods, addressing the inherent variability in inter-event durations. Parameter estimation is performed using the Expectation-Maximization algorithm, with model selection validated via the Bayesian information criterion (BIC). To complement the parametric approach, Kaplan-Meier survival analysis was employed to provide non-parametric insights into storm-free intervals. Additionally, a simulation-based framework estimates storm recurrence probabilities and assesses financial risks through probable maximum loss (PML) calculations. The proposed methodology is applied to the Billion-Dollar Weather and Climate Disasters dataset, compiled by the U.S. National Oceanic and Atmospheric Administration (NOAA). The results demonstrate the model's effectiveness in predicting severe storm recurrence intervals, offering valuable tools for managing risk in the property and casualty insurance industry.