Improved Inference for the XLindley Distribution: A Comparative Analysis of Confidence Intervals and Applications

Abstract

The XLindley distribution is a one-parameter lifetime distribution obtained as a mixture of the exponential and Lindley distributions and is suitable for modeling positively skewed reliability and survival data. Despite its wide applicability, confidence interval (CI) estimation for its parameter has not been adequately studied. This paper proposes four CI estimation methods for the XLindley distribution parameter: the likelihood-based CI, Wald-type CI, bootstrap-t CI, and bias-corrected and accelerated (BCa) bootstrap CI. Their performance is examined through Monte Carlo simulation studies under various sample sizes and parameter values. Empirical coverage probability (ECP) and average width (AW) are used as evaluation criteria. The results indicate that the likelihood-based and Wald-type CIs provide stable and reliable coverage, particularly for small to moderate samples, whereas the bootstrap-t and BCa methods yield narrower intervals but may exhibit undercoverage in small samples. The proposed methods are further illustrated using two real datasets on bladder cancer remission times and light bulb failure times. Model comparison results based on information criteria, goodness-of-fit tests, and graphical analysis confirm the suitability of the XLindley distribution. Overall, the proposed CI methods provide practical tools for inference in lifetime data analysis.