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Inference about the shape parameters of several inverse Gaussian distributions: testing equality and confidence interval for a common value

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  • Mohammad Reza Kazemi

    (Fasa University)

  • Ali Akbar Jafari

    (Yazd University)

Abstract

In this paper, we consider inference about the shape parameters of several inverse Gaussian distributions. At first, an approach is given to test the equality of these parameters based on modified likelihood ratio test. Then, five approaches are presented to construct confidence intervals for the common shape parameter. The performance of these approaches is studied using Monte Carlo simulation, and illustrated using a real data set.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:5:d:10.1007_s00184-018-0693-9
    DOI: 10.1007/s00184-018-0693-9
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    References listed on IDEAS

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    1. Seshadri, V, 1988. "A U-statistic and estimation for the inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 7(1), pages 47-49, July.
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    4. 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.
    5. Tore Schweder & Nils Lid Hjort, 2002. "Confidence and Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(2), pages 309-332, June.
    6. S. Lin, 2013. "The higher order likelihood method for the common mean of several log-normal distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 381-392, April.
    7. 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.
    8. Liu, Xuhua & Li, Na & Hu, Yuqin, 2015. "Combining inferences on the common mean of several inverse Gaussian distributions based on confidence distribution," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 136-142.
    9. Chaubey, Yogendra P. & Sen, Debaraj & Saha, Krishna K., 2014. "On testing the coefficient of variation in an inverse Gaussian population," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 121-128.
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    Cited by:

    1. 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.

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