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On estimating common mean of several inverse Gaussian distributions

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  • Samadrita Bera

    (Indian Institute of Technology (ISM), Dhanbad)

  • Nabakumar Jana

    (Indian Institute of Technology (ISM), Dhanbad)

Abstract

Estimation of the common mean of inverse Gaussian distributions with different scale-like parameters is considered. We study finite sample properties, second-order admissibility and Pitman closeness properties of the Graybill–Deal estimator of the common mean. The best asymptotically normal estimator of the common mean is derived when the coefficients of variations are known. When the scale-like parameters are unknown but ordered, an improved estimator of the common mean is proposed. We also derive estimators of the common mean using the modified profile likelihood method. A simulation study has been performed to compare among the estimators.

Suggested Citation

  • Samadrita Bera & Nabakumar Jana, 2022. "On estimating common mean of several inverse Gaussian distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 115-139, January.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:1:d:10.1007_s00184-021-00829-y
    DOI: 10.1007/s00184-021-00829-y
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    References listed on IDEAS

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    1. Tatsuya Kubokawa, 1989. "Closer estimators of a common mean in the sense of Pitman," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(3), pages 477-484, September.
    2. Mohammad Reza Kazemi & Ali Akbar Jafari, 2019. "Inference about the shape parameters of several inverse Gaussian distributions: testing equality and confidence interval for a common value," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(5), pages 529-545, July.
    3. Cuizhen Niu & Xu Guo & Wangli Xu & Lixing Zhu, 2014. "Testing equality of shape parameters in several inverse Gaussian populations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 795-809, August.
    4. Tian, Lili, 2006. "Testing equality of inverse Gaussian means under heterogeneity, based on generalized test variable," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1156-1162, November.
    5. Manzoor Ahmad & Y. Chaubey & B. Sinha, 1991. "Estimation of a common mean of several univariate inverse Gaussian populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 357-367, June.
    6. Ventura, Laura & Cabras, Stefano & Racugno, Walter, 2009. "Prior Distributions From Pseudo-Likelihoods in the Presence of Nuisance Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 768-774.
    7. Yuan-Tsung Chang & Nobuo Shinozaki, 2015. "Estimation of two ordered normal means under modified Pitman nearness criterion," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 863-883, October.
    8. Tiefeng Ma & Shuangzhe Liu & S. Ahmed, 2014. "Shrinkage estimation for the mean of the inverse Gaussian population," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 733-752, August.
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    Cited by:

    1. Mahmoud Aldeni & John Wagaman & Mohamed Amezziane & S. Ejaz Ahmed, 2023. "Pretest and shrinkage estimators for log-normal means," Computational Statistics, Springer, vol. 38(3), pages 1555-1578, September.

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