On Truncated XLindley Distribution: Statistical Properties, Estimation Methods, and Application in Sciences

Abstract

This study investigates the statistical properties and practical utility of the truncated variants of the X-Lindley distribution. Key distributional characteristics such as the probability density function and hazardrate function are examined, highlighting their consistent and flexible behavior. Several statistical measuresare derived, including moments, quantile functions, and associated metrics, offering a comprehensive un-derstanding of the model. Estimation of parameters is conducted using the maximum likelihood estimation(MLE) method, specifically tailored for the truncated form. To validate the proposed models, a real datasetconcerning the strength of aircraft window glass is analyzed, demonstrating the improved fit and applicabilityof the truncated X-Lindley distribution in reliability and survival data contexts.The results underscore the distribution’s potential for modeling truncated lifetime data and its relevancein engineering and insurance applications. Additionally, this contribution explores the statistical character-istics and real-world applications of the truncated X-Lindley distribution in the context of actuarial science.The practical utility of this distribution is demonstrated through its application to truncated age-at-deathdata relevant to life insurance pricing. Comparative analysis with traditional and modern models such as theExponential, Weibull, Truncated Weibull, Truncated Lindley, Truncated Gamma, Truncated Exponential,and Truncated Log-Normal distributions reveals that the truncated X-Lindley model provides a superior fitand more accurate estimation of the Net Single Premium (NSP). These results highlight the effectivenessof the proposed model in life insurance valuation and its potential for broader use in actuarial and survivaldata analysis.Furthermore, the study introduces a reliability analysis using the truncated X-Lindley distribution formachine failure time data. This analysis demonstrates the model’s suitability for predicting failure times inengineering applications, showcasing its versatility across different sectors.