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<p>In this study, entropy estimation for the versatile inverse generalized gamma (IGG) distribution, a model well-suited for analyzing lifetime and highly skewed data, is explored. The IGG parameters are estimated using the maximum likelihood method to compute both the Shannon and the Rényi entropies. For a Bayesian approach, squared error, linear exponential, and precautionary loss functions are employed to derive entropy estimates. Due to the absence of closed-form posterior distributions, the Hamiltonian Monte Carlo No-U-Turn Sampler is utilized for efficient posterior sampling. The practical application and effectiveness of these estimation methods are demonstrated through the analysis of aircraft windshield failures for estimating entropies.</p>

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Bayesian Estimation of Some Entropies and their Application in Aircraft Windshields

  • 期刊论文

  • 发表日期：

    2026年4月10日

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  • Dhiraj Kumar Singh,
  • Himanshu Bhatt

摘要

In this study, entropy estimation for the versatile inverse generalized gamma (IGG) distribution, a model well-suited for analyzing lifetime and highly skewed data, is explored. The IGG parameters are estimated using the maximum likelihood method to compute both the Shannon and the Rényi entropies. For a Bayesian approach, squared error, linear exponential, and precautionary loss functions are employed to derive entropy estimates. Due to the absence of closed-form posterior distributions, the Hamiltonian Monte Carlo No-U-Turn Sampler is utilized for efficient posterior sampling. The practical application and effectiveness of these estimation methods are demonstrated through the analysis of aircraft windshield failures for estimating entropies.