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Three-stage estimation of the mean and variance of the normal distribution with application to an inverse coefficient of variation with computer simulation
(MDPI AG, 2019) Yousef A.; Hamdy H.; Department of Mathematics; Kuwait College of Science and Technology; Kuwait City; 27235; Kuwait; Faculty of Management Sciences; October University for Modern Sciences and Arts; 6th October City; 12566; Egypt
This 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.