Abstract
A characterization of the generalized inverse Gaussian population is obtained from a condition of constant regression of a suitable statistic on a linear one.
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References
Barndorff-Nielsen, O. and Halgreen, Ch. (1977). Infinite divisibility of the hyperbolic and generalized inverse Gaussian distributions, Zeit. Wahrscheinlichkeitsth., 38, 309–311.
Bolger, E. M. and Harkness, W. L. (1965). Characterization of some distributions by conditional moments, Ann. Math. Statist., 36, 703–705.
Gordon, F. S. (1973). Characterizations of populations using regression properties, Ann. Statist., 1(1), 114–126.
Kagan, A. M., Linnik, Y. V. and Rao, C. R. (1973). Characterization Problems in Mathematical Statistics, Wiley, New York.
Khatri, C. G. (1962). A characterization of the inverse Gaussian distribution, Ann. Math. Statist., 33, 800–803.
Laha, R. G. and Lukacs, E. (1960). On some characterization problems connected with quadratic regression, Biometrika, 47, 335–343.
Roy, L. K. and Wasan, M. T. (1969). A characterization of the inverse Gaussian distribution, Sankhyä Ser. A, 31, 217–218.
Seshadri, V. (1983). The inverse Gaussian distribution: some properties and characterizations, Canad. J. Statist., 11(2), 131–136.
Seshadri, V. (1993). The inverse Gaussian distribution, Clarendon Press, Oxford.
Tweedie, M. C. K. (1957). Statistical properties of inverse Gaussian distributions. I, Ann. Math. Statist., 28, 362–377.
Watson, G. N. (1958). A Treatise of the Theory of Bessel Functions, University Press, Cambridge.
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Pusz, J. Regressional Characterization of the Generalized Inverse Gaussian Population. Annals of the Institute of Statistical Mathematics 49, 315–319 (1997). https://doi.org/10.1023/A:1003167030482
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DOI: https://doi.org/10.1023/A:1003167030482