The New Two-Parameter Exponential-Gamma-Based Distribution: Properties and Application to Non-Communicable Disease Data

Abstract

This study introduces a novel lifetime distribution, termed the New Two-Parameter Exponential–Gamma (NTPEG) distribution, developed through an additive mixture framework to enhance flexibility in modeling lifetime and survival data. Fundamental structural properties, including moments, hazard rate behavior, and entropy, are derived and discussed. Parameters of the model are estimated via the maximum likelihood method, and simulation studies demonstrate the reliability and efficiency of the estimators. The practical utility of the NTPEG model is illustrated using survival data on non-communicable diseases, particularly among acute bone cancer patients. Comparative analyses with existing extensions of the Lindley distribution reveal that the proposed model provides superior fit and flexibility for complex real-world data. Overall, the NTPEG distribution represents a robust and versatile tool for researchers and practitioners in survival and reliability analysis.