The Weighted Sanni–Lindley Distribution: A Flexible Model for Reliability and Failure Time Analysis

Abstract

The Lindley distribution has been widely applied in reliability and survival analysis; however, its limited flexibility often restricts its ability to adequately model complex lifetime data. To address this limitation, this study introduces a new three-parameter lifetime model, termed the Weighted Sanni–Lindley Distribution (WSLD), obtained by incorporating a weighting mechanism into the recently proposed Sanni distribution framework. The additional parameter enhances the model's flexibility and enables it to accommodate a broader range of distributional shapes and failure-rate behaviours encountered in reliability studies. Fundamental statistical properties of the proposed distribution are derived, including its probability density function, cumulative distribution function, moments, survival function, hazard rate function, Rényi entropy, and order statistics. Parameter estimation is carried out using the method of maximum likelihood, and the corresponding Fisher information matrix is established to facilitate statistical inference and confidence interval construction. Furthermore, a comprehensive Monte Carlo simulation study is conducted to evaluate the finite-sample performance of the maximum likelihood estimators in terms of bias, mean squared error, and standard deviation. The practical applicability of the model is demonstrated using two real-life datasets involving aircraft windshield failures and glass fibre strengths. Comparative analyses based on log-likelihood, AIC, AICc, and BIC reveal that the proposed WSLD consistently provides a superior fit relative to competing lifetime distributions, thereby offering a robust and flexible framework for reliability and survival data modelling.