An Updated Lindley Distribution: Properties, Estimation, Acceptance Sampling, Actuarial Risk Assessment and Applications

Abstract

This paper introduces the updated Lindley (UL) distribution, an innovative mixture of exponential and gamma distributions designed to model lifetime data with various failure rate patterns. The statistical properties of the UL distribution, including moments, skewness, kurtosis, and tail behavior, are thoroughly examined to highlight its flexibility and applicability. Parameter estimation methods using non-Bayesian are evaluated for their accuracy using bias and mean squared error metrics across various scenarios. The paper further explores applications of the UL distribution in acceptance sampling plans, actuarial risk assessment, and reliability analysis. Comprehensive simulation studies and graphical visualizations underscore the robustness and versatility of the distribution in addressing real-world problems, making it a valuable tool in statistical modeling and decision-making processes.