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On the exact distribution of the likelihood ratio test statistic for testing the homogeneity of the scale parameters of several inverse Gaussian distributions

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  • Mahmood Kharrati-Kopaei

    (Shiraz University)

Abstract

Several researchers have addressed the problem of testing the homogeneity of the scale parameters of several independent inverse Gaussian distributions based on the likelihood ratio test. However, only approximations of the distribution function of the test statistic are available in the literature. In this note, we present the exact distribution of the likelihood ratio test statistic for testing the equality of the scale parameters of several independent inverse Gaussian populations in a closed form. To this end, we apply the Mellin inverse transform and the Jacobi polynomial expansion to the moments of the likelihood ratio test statistic. We also propose an approximate method based on the Jacobi polynomial expansion. Finally, we apply an accurate numerical method, which is based on the inverse of characteristic function, to obtain a near-exact approximation of the likelihood ratio test statistic distribution. The proposed methods are illustrated via numerical and real data examples.

Suggested Citation

  • Mahmood Kharrati-Kopaei, 2021. "On the exact distribution of the likelihood ratio test statistic for testing the homogeneity of the scale parameters of several inverse Gaussian distributions," Computational Statistics, Springer, vol. 36(2), pages 1123-1138, June.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-01053-4
    DOI: 10.1007/s00180-020-01053-4
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    References listed on IDEAS

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    1. Viktor Witkovsky & Gejza Wimmer & Tomas Duby, 2017. "Computing the aggregate loss distribution based on numerical inversion of the compound empirical characteristic function of frequency and severity," Papers 1701.08299, arXiv.org.
    2. Robert J. Boik, 1993. "Null Distribution of a Statistic for Testing Sphericity and Additivity: A Jacobi Polynomial Expansion," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(3), pages 567-576, September.
    3. Robert B. Davies, 1980. "The Distribution of a Linear Combination of χ2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 323-333, November.
    4. 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.
    5. Mahmood Kharrati-Kopaei & Ahad Malekzadeh, 2019. "On the exact distribution of the likelihood ratio test for testing the homogeneity of scale parameters of several two-parameter exponential distributions: complete and censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 409-427, May.
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