Seng Huat Ong

Modeling bivariate count data with complex dispersion and dependence structures remains a significant challenge in statistical data analysis. This article introduces two new bivariate count distributions derived from the generalized shifted inverse trinomial distribution. The proposed models, denoted by BGIT-I and BGIT-II, are constructed using convolution and trivariate reduction methods. They provide flexible joint frameworks for modeling correlated count data while accommodating different marginal dispersion patterns. BGIT-I allows negative, near-zero, and positive dependence, whereas BGIT-II induces non-negative dependence through a common component. The proposed models have simple, tractable probability generating functions, which facilitate the derivation of probabilistic properties and motivate a probability-generating-function-based estimation approach alongside maximum-likelihood estimation. The finite-sample performance of the estimators is further examined through a Monte Carlo simulation study. The practical utility of the proposed models is illustrated using two real bivariate count data sets involving shunter accidents and patient counts in critical care and emergency room settings. The results show that the proposed BGIT models provide competitive alternatives for modeling bivariate count data with different dispersion and dependence characteristics.

The vulnerability of transmitted digital images has become a pressing concern due to recent advancements in multimedia technology. Conventional encryption methods often fail to meet the requirements of large-scale real-time multimedia security. In order to strengthen color image encryption, in this paper, we propose a novel encryption method that combines fuzzy cellular neural networks with dynamic audio-based biometric data, which aligns with the principle of symmetric encryption. To make the encryption process specific to each user and hard to replicate, the method uses speech characteristics—the peak frequency and zero-crossing rate—extracted from the user’s voice. By integrating these voice features into the fuzzy cellular neural network structure, the method expands the set of potential keys and enhances protection against brute-force, statistical, and chosen-plaintext attacks. Compared to conventional methods that rely solely on chaotic maps or neural networks, this approach provides a larger key space, higher entropy, and better disruption of pixel correlation. The encryption quality is validated through experimental results using the NPCR, UACI, PSNR, and SSIM metrics. Securing multimedia transmissions contributes to the broader vision of a protected society, where technological progress promotes safety, trust, and fair access to knowledge.

This article introduces a flexible time series regression model known as the Mixture of Integer-Valued Generalized Autoregressive Conditional Heteroscedasticity (MINGARCH). Mixture models provide versatile frameworks for capturing heterogeneity in count data, including features such as multiple peaks, seasonality, and intervention effects. The proposed model is applied to regional COVID-19 data from Malaysia. To account for geographical variability, five regions—Selangor, Kuala Lumpur, Penang, Johor, and Sarawak—were selected for analysis, covering a total of 86 weeks of data. Comparative analysis with existing time series regression models demonstrates that MINGARCH outperforms alternative approaches. Further investigation into forecasting reveals that MINGARCH yields superior performance in regions with high population density, and significant influencing factors have been identified. In low-density regions, confirmed cases peaked within three weeks, whereas high-density regions exhibited a monthly seasonal pattern. Forecasting metrics—including MAPE, MAE, and RMSE—are significantly lower for the MINGARCH model compared to other models. These results suggest that MINGARCH is well-suited for forecasting disease spread in urban and densely populated areas, offering valuable insights for policymaking.