Abstract: This paper introduces a robust statistical framework for analyzing lifetime data using the Kumaraswamy Weibull Frechet [KWFR) distribution under Type II censoring. The KWFR distribution is a flexible composite model that integrates the Kumaraswamy, Weibull, and Frechet distributions, enabling the modeling of data with heavy tails and extreme events. Type II censoring, commonly employed in reliability and survival studies, involves observing the smallest failure times from a total of units, with the remaining observations censored. The study derives the likelihood function for the KWFR distribution based on Type II censored samples and applies the Maximum Likelihood Estimation (MLE) method to estimate its parameters. Analytical techniques are employed to handle the complexity of the model, supported by numerical optimization methods to ensure accurate parameter estimation. The properties of the MLE, including consistency and asymptotic efficiency, are discussed, emphasizing its effectiveness in capturing the distribution's underlying characteristics even with incomplete data. Additionally, Bayesian estimation methods are explored, employing gamma priors for unknown parameters within a Squared loss function and LINEX loss function. The Metropolis-Hasting algorithm is utilized as part of the Markov Chain Monte Carlo technique to obtain Bayesian estimates. The proposed methodology is validated through simulation studies, demonstrating the flexibility and robustness of the KWFR distribution in modeling lifetime data under various censoring scenarios. Additionally, the practical utility of the model is illustrated with real-world datasets, highlighting its potential applications in reliability engineering, risk assessment, and environmental studies. This research provides a significant contribution to the statistical modeling of censored data, offering insights into the behavior of complex lifetime distributions.

Keywords: Kumaraswamy Weibull Frechet distribution, Type II censoring, Maximum Likelihood Estimation, reliability analysis, survival studies, Bayesian Estimation

Pages: 14-38

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