Reliability and estimation of the zero-inflated transmuted geometric distribution with applications and actuarial insights

This article delves into the zero-inflated transmuted geometric distribution, a novel approach to modeling count data with excess zeros. The study explores the distribution's properties, including its probability mass function, cumulative distribution function, and hazard rate function, which can exhibit increasing, decreasing, constant, and bath-tub shaped patterns. The article also discusses the distribution's applications in reliability and actuarial science, providing insights into its practical utility. Through simulations and real-life datasets, the authors demonstrate the distribution's effectiveness in fitting complex datasets, offering a better fit compared to other count models. The likelihood ratio test further strengthens the theory, confirming the distribution's superiority. This comprehensive analysis makes the zero-inflated transmuted geometric distribution a valuable tool for professionals dealing with count data in various fields.