Bayesian and non-Bayesian inference for the inverse power induced XLindley distribution with applications to engineering and radiation data

The two-parameter distribution of the inverse power induced XLindley (IPIXLN) model is a novel model that outperforms conventional distributions and is presented in this study. The new distribution offers a remarkably rich set of probability functions compared to the current ones. Features of the density and hazard rate functions show that the model can be applied to a wide range of data types. The quantile function, Rényi entropy, moments with some related measures, and order statistics are among the mathematical characteristics of the proposed distribution that are examined in this paper. Thorough Monte Carlo simulation, research compares the efficacy of several estimation strategies used to estimate the model parameters, including maximum likelihood estimation (MLE), Bayesian estimation (BE), and maximum product of spacings (MPS). The suggested IPIXLN model is fitted to two real-world datasets from the engineering and radiation domains to show its usefulness. The findings show that, in comparison to well-known distributions, the suggested model offers a better fit and more flexibility. All things considered, the results demonstrate how well the IPIXLN model describes lifetime and reliability data and is a broad, mathematically tractable, and highly flexible model that contributes significantly to the family of continuous probability distributions.