Vol.:(0123456789) Annals of Data Science https://doi.org/10.1007/s40745-020-00320-x 1 3 E‑Bayesian and Hierarchical Bayesian Estimations for the Inverse Weibull Distribution Abdulkareem M. Basheer 1,4  · H. M. Okasha 2,5  · A. H. El‑Baz 3  · A. M. K. Tarabia 1 Received: 15 June 2020 / Revised: 14 November 2020 / Accepted: 18 December 2020 © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract In this paper new formulas for E-Bayesian and hierarchical Bayesian estimations of the parameter and reliability of the inverse Weibull distribution are obtained in closed forms. To illustrate the applicability of the obtained results, simulated and real data are used which illustrate that E-Bayesian estimate gives superior perfor- mance much better than hierarchical Bayesian for the estimate of the parameter of the inverse Weibull distribution. Keywords Inverse Weibull distribution · E-Bayesian estimation · Hierarchical Bayesian estimation · Reliability · Simulation 1 Introduction Recently, data scientists have been addressing questions about the future. They start with big data that features three measures: volume, variety, and speed. Also, they use it as fodder for algorithms and models. Also, they changed nearly every industry. For example, in medicine their algorithms help predict side efects for a patient. In sports science, their models and measures have redefned “athletic potential”. Tackle the trafc, too, with road improvement models that capture the usual rush hours and the quiet of the weekend. In the feld of machine learning * Abdulkareem M. Basheer abdulkareem_basheer@yahoo.com 1 Department of Mathematics, Faculty of Science, Damietta University, Damietta, Egypt 2 Department of Statistics, Faculty of Science, King AbdulAziz University, Jeddah, Saudi Arabia 3 Department of Computer Science, Faculty of Computers and Information, Damietta University, Damietta, Egypt 4 Present Address: Al-Bayda University, Al-Bayda, Yemen 5 Present Address: Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt Content courtesy of Springer Nature, terms of use apply. Rights reserved.