Negative Binomial Two-Parameter Lindley generalized linear model for modeling count data - Samwel Karanja Kamau; Cox Lwaka Tamba; Luke Akong’o Orawo; Justin Obwoge Okenye (Research in Statistics)
Zero-inflated data, characterized by excessive zero counts, is a common challenge in various fields, particularly in insurance data. In most cases, count data exhibits overdispersion and excess zeros; models that fail to account for these characteristics lead to biased estimates. In this paper, a Negative Binomial Two-Parameter Lindley (NBTPL) generalized linear model (GLM) was developed, and the Bayesian framework was considered when estimating the model parameters. The performance of the developed model was compared with existing GLMs, specifically Zero-Inflated Negative Binomial (ZINB), Hurdle Negative Binomial (HNB), and Negative Binomial-Lindley (NBL) models. Model fit was assessed using Akaike Information Criterion (AIC) and Mean Squared Error (MSE) values. In simulation study, the NBTPL model outperforms existing models in explaining count data that are over-dispersed and zero-inflated. The GLM based on the NBTPL model had the lowest AIC and MSE values. The NBTPL GLM was applied to analyze real data on claim frequencies based on Kenyan insurance industry data. Claim frequency data usually exhibits zero inflation, overdispersion, and relative long-tail characteristics. From the real data analysis, gender, age of the policyholders, and the type of insurance policy were the determinants of insurance claims. NBTPL GLM model is recommended for zero-inflated, over-dispersed count data.