IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v82y2019i5d10.1007_s00184-018-0693-9.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-018-0693-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-018-0693-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ib M. Skovgaard, 2001. "Likelihood Asymptotics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 3-32, March.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Seshadri, V, 1988. "A U-statistic and estimation for the inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 7(1), pages 47-49, July.
    9. K. Krishnamoorthy & Meesook Lee, 2014. "Improved tests for the equality of normal coefficients of variation," Computational Statistics, Springer, vol. 29(1), pages 215-232, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. 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.
    3. Wong ACM & Zhang S, 2017. "A Directional Approach for Testing Homogeneity of Inverse Gaussian Scale-Like Parameters," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 3(2), pages 34-39, September.
    4. David R. Bickel, 2024. "Bayesian and frequentist inference derived from the maximum entropy principle with applications to propagating uncertainty about statistical methods," Statistical Papers, Springer, vol. 65(8), pages 5389-5407, October.
    5. La Vecchia, Davide & Moor, Alban & Scaillet, Olivier, 2023. "A higher-order correct fast moving-average bootstrap for dependent data," Journal of Econometrics, Elsevier, vol. 235(1), pages 65-81.
    6. Cristine Rauber & Francisco Cribari-Neto & Fábio M. Bayer, 2020. "Improved testing inferences for beta regressions with parametric mean link function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 687-717, December.
    7. V. Filimonov & G. Demos & D. Sornette, 2017. "Modified profile likelihood inference and interval forecast of the burst of financial bubbles," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1167-1186, August.
    8. Xiaokang Luo & Tirthankar Dasgupta & Minge Xie & Regina Y. Liu, 2021. "Leveraging the Fisher randomization test using confidence distributions: Inference, combination and fusion learning," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 777-797, September.
    9. Melo, Tatiane F.N. & Vasconcellos, Klaus L.P. & Lemonte, Artur J., 2009. "Some restriction tests in a new class of regression models for proportions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3972-3979, October.
    10. Nicolas Miconnet & Marie Cornu & Annie Beaufort & Laurent Rosso & Jean‐Baptiste Denis, 2005. "Uncertainty Distribution Associated with Estimating a Proportion in Microbial Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 25(1), pages 39-48, February.
    11. Erlis Ruli & Laura Ventura, 2021. "Can Bayesian, confidence distribution and frequentist inference agree?," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 359-373, March.
    12. Sadooghi-Alvandi, Soltan Mohammad & Malekzadeh, Ahad, 2013. "A note on testing homogeneity of the scale parameters of several inverse Gaussian distributions," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1844-1848.
    13. Piero Veronese & Eugenio Melilli, 2021. "Confidence Distribution for the Ability Parameter of the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 131-166, March.
    14. Ole E. Barndorff-Nielsen & Bent Nielsen & Neil Shephard & Carla Ysusi, 2002. "Measuring and forecasting financial variability using realised variance with and without a model," Economics Papers 2002-W21, Economics Group, Nuffield College, University of Oxford.
    15. Chang, Ming & You, Xuqun & Wen, Muqing, 2012. "Testing the homogeneity of inverse Gaussian scale-like parameters," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1755-1760.
    16. Rukhin, Andrew L., 2016. "Confidence regions for comparison of two normal samples," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 273-280.
    17. A. C. Davison & D. A. S. Fraser & N. Reid & N. Sartori, 2014. "Accurate Directional Inference for Vector Parameters in Linear Exponential Families," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 302-314, March.
    18. Kruschke, John K. & Liddell, Torrin, 2016. "The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective," OSF Preprints ksfyr, Center for Open Science.
    19. Yang Liu & Jan Hannig, 2017. "Generalized Fiducial Inference for Logistic Graded Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1097-1125, December.
    20. Bickel David R., 2012. "Empirical Bayes Interval Estimates that are Conditionally Equal to Unadjusted Confidence Intervals or to Default Prior Credibility Intervals," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-34, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:82:y:2019:i:5:d:10.1007_s00184-018-0693-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.