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

Mahmood Kharrati-Kopaei ()
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Mahmood Kharrati-Kopaei: Shiraz University

Computational Statistics, 2021, vol. 36, issue 2, No 14, 1123-1138

Abstract: 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.

Keywords: Analysis of reciprocals; Characteristic function; Jacobi polynomial expansion; Inverse Gaussian; Mellin inverse transform (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00180-020-01053-4

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