IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v79y2017i2d10.1007_s13571-017-0136-z.html
   My bibliography  Save this article

Symmetrizing and Variance Stabilizing Transformations of Sample Coefficient of Variation from Inverse Gaussian Distribution

Author

Listed:
  • Yogendra P. Chaubey

    (Department of Mathematics and Statistics, Concordia University)

  • Murari Singh

    (International Center for Agricultural Research in the Dry Areas)

  • Debaraj Sen

    (Department of Mathematics and Statistics, Concordia University)

Abstract

Coefficient of variation (CV) plays an important role in statistical practice; however, its sampling distribution may not be easy to compute. In this paper, the distributional properties of the sample CV from an inverse Gaussian distribution are investigated through transformations. Specifically, the symmetrizing transformation as outlined in Chaubey and Mudholkar (1983), that requires numerical techniques, is contrasted with the explicitly available variance stabilizing transformation (VST). The symmetrizing transformation scores very high as compared to the VST, especially in a power family. The usefulness of the resulting approximation is illustrated through a numerical example.

Suggested Citation

  • Yogendra P. Chaubey & Murari Singh & Debaraj Sen, 2017. "Symmetrizing and Variance Stabilizing Transformations of Sample Coefficient of Variation from Inverse Gaussian Distribution," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 217-246, November.
  • Handle: RePEc:spr:sankhb:v:79:y:2017:i:2:d:10.1007_s13571-017-0136-z
    DOI: 10.1007/s13571-017-0136-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-017-0136-z
    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/s13571-017-0136-z?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. Govind Mudholkar & Rajeshwari Natarajan, 2002. "The Inverse Gaussian Models: Analogues of Symmetry, Skewness and Kurtosis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 138-154, March.
    2. 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.
    3. David Hinkley, 1977. "On Quick Choice of Power Transformation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 67-69, March.
    4. Norbert Henze & Bernhard Klar, 2002. "Goodness-of-Fit Tests for the Inverse Gaussian Distribution Based on the Empirical Laplace Transform," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 425-444, June.
    Full references (including those not matched with items on IDEAS)

    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. José A. Villaseñor & Elizabeth González-Estrada & Adrián Ochoa, 2019. "On Testing the Inverse Gaussian Distribution Hypothesis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 60-74, June.
    2. Ramadan A. ZeinEldin & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy, 2019. "Statistical Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution," Mathematics, MDPI, vol. 7(10), pages 1-24, October.
    3. Leiva, Víctor & Hernández, Hugo & Sanhueza, Antonio, 2008. "An R Package for a General Class of Inverse Gaussian Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 26(i04).
    4. Ammara Tanveer & Muhammad Azam & Muhammad Aslam & Muhammad Shujaat Navaz, 2020. "Attribute np control charts using resampling systems for monitoring non-conforming items under exponentiated half-logistic distribution," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(2), pages 115-143.
    5. Adolfo Quiroz & Miguel Nakamura & Francisco Pérez, 1996. "Estimation of a multivariate Box-Cox transformation to elliptical symmetry via the empirical characteristic function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 687-709, December.
    6. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "A new test of multivariate normality by a double estimation in a characterizing PDE," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 401-427, April.
    7. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.
    8. Bojana Milošević & Marko Obradović, 2016. "New class of exponentiality tests based on U-empirical Laplace transform," Statistical Papers, Springer, vol. 57(4), pages 977-990, December.
    9. Guerrero, Victor M. & Solis-Lemus, Claudia, 2020. "A generalized measure of dispersion," Statistics & Probability Letters, Elsevier, vol. 164(C).
    10. Ayush Tripathi & Umesh Singh & Sanjay Kumar Singh, 2021. "Inferences for the DUS-Exponential Distribution Based on Upper Record Values," Annals of Data Science, Springer, vol. 8(2), pages 387-403, June.
    11. Harsh Tripathi & Varun Agiwal, 2024. "A new version of univariate Rayleigh distribution: properties, estimation and it’s application," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(11), pages 5367-5377, November.
    12. Ausaina Niyomdecha & Patchanok Srisuradetchai, 2023. "Complementary Gamma Zero-Truncated Poisson Distribution and Its Application," Mathematics, MDPI, vol. 11(11), pages 1-13, June.
    13. Mustapha Muhammad & Rashad A. R. Bantan & Lixia Liu & Christophe Chesneau & Muhammad H. Tahir & Farrukh Jamal & Mohammed Elgarhy, 2021. "A New Extended Cosine—G Distributions for Lifetime Studies," Mathematics, MDPI, vol. 9(21), pages 1-29, October.
    14. Majid Hashempour & Morad Alizadeh & Haitham M. Yousof, 2024. "A New Lindley Extension: Estimation, Risk Assessment and Analysis Under Bimodal Right Skewed Precipitation Data," Annals of Data Science, Springer, vol. 11(6), pages 1919-1958, December.
    15. Chakraburty Subrata & Alizadeh Morad & Handique Laba & Altun Emrah & Hamedani G. G., 2021. "A new extension of Odd Half-Cauchy Family of Distributions: properties and applications with regression modeling," Statistics in Transition New Series, Statistics Poland, vol. 22(4), pages 77-100, December.
    16. Lee, Sangyeol & Vonta, Ilia & Karagrigoriou, Alex, 2011. "A maximum entropy type test of fit," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2635-2643, September.
    17. Raed R. Abu Awwad & Omar M. Bdair & Ghassan K. Abufoudeh, 2021. "Bayesian estimation and prediction based on Rayleigh record data with applications," Statistics in Transition New Series, Polish Statistical Association, vol. 22(3), pages 59-79, September.
    18. 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.
    19. Žikica Lukić & Bojana Milošević, 2024. "A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 797-820, October.
    20. Baringhaus, Ludwig & Gaigall, Daniel, 2015. "On an independence test approach to the goodness-of-fit problem," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 193-208.

    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:sankhb:v:79:y:2017:i:2:d:10.1007_s13571-017-0136-z. 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.