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On Testing the Inverse Gaussian Distribution Hypothesis

Author

Listed:
  • José A. Villaseñor

    (Colegio de Postgraduados)

  • Elizabeth González-Estrada

    (Colegio de Postgraduados)

  • Adrián Ochoa

    (Colegio de Postgraduados)

Abstract

The family of Inverse Gaussian (IG) distributions has applications in areas such as hydrology, lifetime testing, and reliability, among others. In this paper, a new characterization for this family of distributions is introduced and is used to propose a test of fit for the IG distribution hypothesis with unknown parameters. As a second test, observations are transformed to normal variables and then Shapiro-Wilk test is used to test for normality. Simulation results show that the proposed tests preserve the nominal test size and are competitive against some existing tests for the same problem. Three real datasets are used to illustrate the application of these tests.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankhb:v:81:y:2019:i:1:d:10.1007_s13571-017-0148-8
    DOI: 10.1007/s13571-017-0148-8
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    References listed on IDEAS

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    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. 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.
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