Classical and Bayesian techniques for modelling engineering dataset using new generalized probability distribution with mathematical features

This paper delves into the investigation of a novel continuous distribution, aiming to provide a thorough understanding of its various fundamental properties. The analysis encompasses an exploration of quantiles, skewness, kurtosis, hazard rate function, moments, incomplete moments, mean deviations, coefficient of variation, mean time to failure, mean time between failure, availability, and reliability functions within the context of consecutive linear and circular systems. Both maximum likelihood and Bayesian methods are employed for parameter estimation to ensure a comprehensive approach. The performance of the estimators is rigorously evaluated through a detailed simulation study, which meticulously considers bias and mean square error metrics. Furthermore, the significance of the new distribution is substantiated through the analysis of real-world datasets, offering practical insights into its applicability and potential advantages in various scenarios. This comprehensive approach not only contributes to the understanding of the distribution itself but also provides valuable guidance for its practical implementation and utilization in statistical modeling and analysis.