Comparison between classical and Bayesian estimation with joint Jeffrey’s prior to Weibull distribution parameters in the presence of large sample conditions

Ahmed Mahdi  Salih; Murtadha Mansour Abdullah

doi:https://doi.org/10.59139/stattrans-2024-010

Comparison between classical and Bayesian estimation with joint Jeffrey’s prior to Weibull distribution parameters in the presence of large sample conditions

Ahmed Mahdi Salih Statistics Department, College of Administration and Economics, Wasit University, Iraq ORCID:https://orcid.org/0000-0002-6109-224X , Murtadha Mansour Abdullah Statistics Department, College of Administration and Economics, Wasit University, Iraq ORCID:https://orcid.org/0000-0002-3341-0415 Statistics in Transition new series, vol. 25, 2024, 4, pages: 191-202 Published online: 11 December 2024 https://doi.org/10.59139/stattrans-2024-010 Citation: Salih A.M., Abdullah M.M., 2024. Comparison between classical and Bayesian estimation with joint Jeffrey’s prior to Weibull distribution parameters in the presence of large sample conditions. Statistics in Transition new series, 25(4), pp. 191-202 https://doi.org/10.59139/stattrans-2024-010

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ABSTRACT

Weibull distribution has been considered one of the most common and valuable distributions for building and analyzing good models for lifetime data. Many researchers have studied the properties of Weibull distribution, also in search of the best method to estimate both parameters. In this paper, we proposed a comparison of Weibull distribution parameters under large sample conditions. We chose to study the classical estimation methods of Weibull distribution parameters, including the maximum likelihood estimator and moments estimation (ME). Next, we compared these methods with the Bayesian estimation method (BE) with Jeffrey’s prior function. We validated the proposed study via simulation using both small and large samples. We used mean square errors (MSE) to determine the best estimation method. Our simulation findings suggest that maximum likelihood estimators are reasonably effective when using small sample sizes. In addition, in cases where the sample size is larger, the BE performed more effectively for both scale and shape parameters of the Weibull distribution function.

KEYWORDS

Weibull distribution, classic estimation, Bayesian estimation, Jeffrey’s prior, large sample.

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