@article{Surya2025, 
author = {Hilda Azkiyah Surya and  Sukono and Herlina Napitupulu and Noriszura Ismail},
title = {Nonstationary transition Poisson-Lindley Hidden Markov model for community-based disaster insurance claim},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {10},
pages = {23411-23428},
keywords = {nonstationary, Poisson-Lindley, hidden Markov model, community-based, claim},
url = {https://www.sciopen.com/article/10.3934/math.20251040},
doi = {10.3934/math.20251040},
abstract = {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 (   B  I  C), 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.}
}