Parameter Estimation of a Non-Homogeneous Inverse Rayleigh Process Using Classical, Metaheuristic, and Deep Learning Approaches

One of the problems of reliability engineering, survival analysis, and applied statistics is correct estimation of lifetime distributions. Relevancy of the inverse Rayleigh distribution, where non-monotonic failure rates are considered, has been especially noted, and classical estimation tools are frequently unable to give good estimates in nonlinear, complicated situations. This paper gives comparative research on four estimation methods namely Ordinary Least Squares (OLS), Maximum Likelihood Estimation (MLE), Support Vector Machines (SVM), and Long Short-Term Memory (LSTM) networks in the estimation of the parameters of the inverse Rayleigh process. The performance of these methods was compared in terms of RMSE and AIC criteria using both as well as real-world data which were obtained through simulation experiments. The findings show the superiority of smart computational methods over traditional methods, where SVM was the most accurate and the strongest in all the conditions. Estimation performance was also significantly higher in LSTM than in OLS and MLE, but slightly lower than that of SVM. These results indicate the applied benefits of machine-learning-based methods in dealing with the nonlinear and complex forms of reliability data. The key finding of the present study is that it offers a comparative analysis of traditional and intelligent estimation approaches in a systematic way and demonstrates that the application of machine learning to statistical modelling may contribute to the high performance of the parameter estimation to a significant degree. This article contributes to the research by showing how SVM is better in estimating the inverse Rayleigh parameter, as well as by highlighting the significance of the hybrid statistical-computational methods in the reliability of applications in the real world. Future directions include the experimental use of additional high-level machine learning architectures, hybrids estimation systems and Bayesian approaches in order to achieve further accuracy improvements and understanding.