A Novel Compound G-Family: Statistical Characteristics and Applications to Aircraft Windshield Service Durations and Survival Time Data

The aim of this scientific research is to present a thorough comprehension of the innovative G families of Statistical models incorporating different copulas, elucidating their statistical characteristics, and illustrating their practical utility across various real lifetime data scenarios. Researchers, statisticians, and practitioners stand to gain valuable insights from the findings of this study, as it equips them with the ability to model intricate relationships and employ multivariate data analysis for informed decision-making. The versatility of compound classes of continuous Statistical models makes them instrumental in simulating diverse phenomena. They can be effectively utilized to represent the frequency of accidents within a defined time frame, the duration until system failure, or the financial losses associated with a transaction. The adaptability of these compound models is a significant advantage, enabling them to address a wide array of situations, including those challenging for other models to adequately capture. Furthermore, these models frequently exhibit ease of application and understanding. A significant advantage of utilizing compound classes of continuous Statistical models lies in their capacity to represent the interdependence of two or more continuous random variables. This research introduces and investigates a novel compound G class of Statistical models, derived from the truncated-Poisson distribution following a zero, which subsequently generates Weibull G classes, thereby establishing the foundation for this new compound G family. The statistical properties of this family are meticulously scrutinized, thereby enhancing comprehension of its mathematical foundations.