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<p>This study focuses on the estimation and application of a right-skewed upside-down bathtub shaped distribution for modelling lifetime data, in the presence of Type-II censoring. The distribution works well with the datasets that show heavy-tailed behaviour and non-monotonic failure rates. Here, the classical as well as Bayesian approaches are used to check the behaviour of the parameter of the considered distribution. In classical point estimation, we performed maximum likelihood estimation, while in case of interval estimation asymptotic confidence intervals and bootstrap intervals (namely; Boot “p” and “t”) are calculated. In Bayesian approach, gamma prior is used. In simulation study, Markov Chain Monte Carlo techniques have been used to generate samples from the posterior distribution. The performance of the estimator has been checked through simulation study for evaluating coverage probabilities, mean squared error, and bias for different sizes of samples under Type-II censoring. The proposed methodology is applied on a real-world dataset, proving the adaptability and versatility of the distribution over a range of its domains. The results indicate that the considered distribution provides a robust framework for modelling lifetime data with UBT-shaped hazard rates and heavy-tailed characteristics, even in the presence of Type-II censoring.</p>

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Classical and Bayesian inference for right skewed upside-down bathtub shaped heavy-tailed distribution in presence of Type-II censoring

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Dhanunjaya Rao Dubbereddy,
  • Sandeep Kumar Maurya

摘要

This study focuses on the estimation and application of a right-skewed upside-down bathtub shaped distribution for modelling lifetime data, in the presence of Type-II censoring. The distribution works well with the datasets that show heavy-tailed behaviour and non-monotonic failure rates. Here, the classical as well as Bayesian approaches are used to check the behaviour of the parameter of the considered distribution. In classical point estimation, we performed maximum likelihood estimation, while in case of interval estimation asymptotic confidence intervals and bootstrap intervals (namely; Boot “p” and “t”) are calculated. In Bayesian approach, gamma prior is used. In simulation study, Markov Chain Monte Carlo techniques have been used to generate samples from the posterior distribution. The performance of the estimator has been checked through simulation study for evaluating coverage probabilities, mean squared error, and bias for different sizes of samples under Type-II censoring. The proposed methodology is applied on a real-world dataset, proving the adaptability and versatility of the distribution over a range of its domains. The results indicate that the considered distribution provides a robust framework for modelling lifetime data with UBT-shaped hazard rates and heavy-tailed characteristics, even in the presence of Type-II censoring.