Bayesian and non-Bayesian inference for the induced XLindley distribution with data analysis

Despite the availability of several lifetime distributions for more flexible and accurate models to capture complex features in lifetime data in reliability and environmental science applications, there remains a gap in modeling data with varying failure rates and heavy tails. This study fills this gap by proposing a new one parameter model-the induced XLindley (IXLN) distribution, which was derived using the induced transformation approach applied to the XLindley (XLN) distribution. The behavior of the novel IXLN distribution was investigated and its performance was assessed in comparison with other well-known distributions such as; XLindley, Lindley, Ishita, Ailamujia, and Chris-Jerry distributions. Critical features of the IXLN distribution, including moments, inverse moments, moment generating functions, order statistics, quantile functions, and Rényi entropy were obtained. The maximum likelihood estimation, maximum product of spacing, and Bayesian estimation methods were used to estimate the parameters of the IXLN distribution. A Monte Carlo simulation study was conducted using an effective algorithm to assess the behavior of different estimators. It was found to be a promising alternative for modeling real world datasets. These findings have significant implications for improving the accuracy of statistical modeling in reliability and environmental science. The IXLN model provides a more flexible and reliable framework, offering better performance compared to traditional models such as the XLN distribution, and has potential for wide-ranging applications in real-world data analysis.