Nonstationary transition Poisson-Lindley Hidden Markov model for community-based disaster insurance claim

This study proposes a nonstationary Poisson-Lindley Hidden Markov Model (PL-HMM) as a novel framework for modeling the frequency of community-based disaster insurance claims. The model accounts for both serial dependence and overdispersion in claim counts through hidden risk states, while nonstationary transition probabilities are introduced via a sliding-window mechanism. Parameters are estimated using the Generalized Expectation-Maximization (GEM) algorithm, supported by a theoretical foundation to ensure a monotonic improvement of the complete log-likelihood. The model was simulated using monthly claim frequency data from West Java Province, Indonesia. A comparative analysis against nonstationary Poisson HMMs with varying numbers of hidden states showed that the two-state nonstationary PL-HMM achieved the lowest Bayesian information criterion ( $BIC$), thus indicating the best fit. A sensitivity analysis of sliding-window horizons (12, 24, and 36 months) demonstrated that persistence patterns of claim risk-states remained robust, with horizon changes reflecting alternative risk measurement periods. The results highlight that the proposed model effectively captures time-varying claim risks, particularly the alternation between low- and high-claim periods, while realistically reflecting the empirical dominance of high-claim regimes. Beyond the simulation data, a nonstationary PL-HMM is flexible and applicable to other regions that exhibit overdispersed claim data, making it a valuable framework for adaptive premium design and disaster risk financing in community-based insurance schemes.