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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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ali Yousef & Hosny Hamdy, 2019. "Three-Stage Estimation of the Mean and Variance of the Normal Distribution with Application to an Inverse Coefficient of Variation with Computer Simulation," Mathematics, MDPI, vol. 7(9), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:831-:d:265375
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    References listed on IDEAS

    as
    1. H. Hamdy & N. Mukhopadhyay & M. Costanza & M. Son, 1988. "Triple stage point estimation for the exponential location parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 785-797, December.
    2. N. Mukhopadhyay & A. Padmanabhan, 1993. "A note on three-stage confidence intervals for the difference of locations: The exponential case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 121-128, December.
    3. M. Al-Mahmeed & H. Hamdy, 1990. "Sequential estimation of linear models in three stages," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 37(1), pages 19-36, December.
    4. M. Son & L. Haugh & H. Hamdy & M. Costanza, 1997. "Controlling Type II Error While Constructing Triple Sampling Fixed Precision Confidence Intervals for the Normal Mean," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(4), pages 681-692, December.
    5. N. Mukhopadhyay & A. Mauromoustakos, 1987. "Three-stage estimation procedures for the negative exponential distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 34(1), pages 83-93, December.
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