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<p>This study explores Bayesian estimation techniques for the parameters of the recently introduced Transformed MG-Extended Exponential (TMGEE) distribution. The Bayesian method employs Lindley’s approximation technique and Markov Chain Monte Carlo (MCMC) algorithms based on independent gamma prior densities. Bayesian estimators are derived with loss both symmetric and asymmetric loss functions. The findings indicate that Bayesian estimation, when using the SELF and LINEX loss functions along with the MCMC method, consistently outperforms Maximum Likelihood Estimation (MLE) in terms of precision and accuracy, particularly with small sample sizes. Three real data sets were used to fit the TMGEE model. The Lindley method was applied under the SELF, and the MCMC method utilizing the NUTS implementation of the HMC algorithm was also employed. The estimated densities obtained from both MCMC and Lindley’s approximation showed close agreement, as confirmed by the Kolmogorov-Smirnov (KS) test, Kullback-Leibler (KL) divergence, and Root Mean Squared Error (RMSE). The results suggested that the Bayesian approach using Lindley’s approximation provides a viable and efficient alternative to MCMC for estimating the parameters of the TMGEE distribution.</p>

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Bayesian Estimation of the Transformed MG-Extended Exponential Distribution using Lindley’s Approximation

  • 期刊论文

  • 发表日期：

    2026年2月17日

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  • Addisalem Assaye Menberu,
  • Ayele Taye Goshu

摘要

This study explores Bayesian estimation techniques for the parameters of the recently introduced Transformed MG-Extended Exponential (TMGEE) distribution. The Bayesian method employs Lindley’s approximation technique and Markov Chain Monte Carlo (MCMC) algorithms based on independent gamma prior densities. Bayesian estimators are derived with loss both symmetric and asymmetric loss functions. The findings indicate that Bayesian estimation, when using the SELF and LINEX loss functions along with the MCMC method, consistently outperforms Maximum Likelihood Estimation (MLE) in terms of precision and accuracy, particularly with small sample sizes. Three real data sets were used to fit the TMGEE model. The Lindley method was applied under the SELF, and the MCMC method utilizing the NUTS implementation of the HMC algorithm was also employed. The estimated densities obtained from both MCMC and Lindley’s approximation showed close agreement, as confirmed by the Kolmogorov-Smirnov (KS) test, Kullback-Leibler (KL) divergence, and Root Mean Squared Error (RMSE). The results suggested that the Bayesian approach using Lindley’s approximation provides a viable and efficient alternative to MCMC for estimating the parameters of the TMGEE distribution.