Estimation of Parameters for a New Model: Real Data Application and Simulation

Effective analysis of survival and renewable energy data is essential to understand complex engineering phenomena. Probability distribution models offer a structured approach to uncovering patterns in such data, particularly for studying disease progression, survival analysis, and many more. In this study, we explore a novel probability distribution using the Harris extended transformation based on the Rayleigh distribution. We thoroughly investigate the statistical properties of the proposed model and derive key reliability measures to demonstrate its applicability in reliability analysis. To ensure precise parameter estimation, the maximum likelihood estimation method is evaluated, and its effectiveness is assessed through a detailed simulation study to confirm the reliability and consistency of its parameters. The practical applicability of the developed model is demonstrated with an analysis of engineering and energy data sets, comparing its performance with several well-known distributions. The results highlight the flexibility and precision of the model, establishing it as a powerful and reliable tool for advanced statistical analysis in survival and engineering research.