Three-Stage Estimation of the Mean and Variance of the Normal Distribution with Application to an Inverse Coefficient of Variation with Computer Simulation

Ali Yousef and Hosny Hamdy
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Ali Yousef: Department of Mathematics, Kuwait College of Science and Technology, Kuwait City 27235, Kuwait
Hosny Hamdy: Faculty of Management Sciences, October University for Modern Sciences and Arts, 6th October City 12566, Egypt

Mathematics, 2019, vol. 7, issue 9, 1-15

Abstract: 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.

Keywords: asymptotic regret; loss function; normal distribution; three-stage sampling procedure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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