Yousef A.Hamdy H.Department of MathematicsKuwait College of Science and TechnologyKuwait City27235Kuwait; Faculty of Management SciencesOctober University for Modern Sciences and Arts6th October City12566Egypt2020-01-092020-01-09201922277390https://doi.org/10.3390/math7090831PubMed ID :https://t.ly/GrpN9ScopusThis paper considers sequentially two main problems. First, we estimate both the mean and the variance of the normal distribution under a unified one decision framework using Hall's three-stage procedure. We consider a minimum risk point estimation problem for the variance considering a squared-error loss function with linear sampling cost. Then we construct a confidence interval for the mean with a preassigned width and coverage probability. Second, as an application, we develop Fortran codes that tackle both the point estimation and confidence interval problems for the inverse coefficient of variation using a Monte Carlo simulation. The simulation results show negative regret in the estimation of the inverse coefficient of variation, which indicates that the three-stage procedure provides better estimation than the optimal. � 2019 by the authors.EnglishOctober University for Modern Sciences and Artsجامعة أكتوبر للعلوم الحديثة والآدابUniversity of Modern Sciences and ArtsMSA UniversityAsymptotic regretLoss functionNormal distributionThree-stage sampling procedureArticlehttps://doi.org/10.3390/math7090831PubMed ID :