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On the domain of partial attraction of semi-stable distributions

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References

  1. Doeblin, W. (1940). Sur l'ensemble de puissances d'une loi de probabilité,Studia Math.,9, 71–96.

    MATH  MathSciNet  Google Scholar 

  2. Feller, W. (1966).An Introduction to Probability Theory and its Applications II, John Wiley, New York.

    MATH  Google Scholar 

  3. Gnedenko, B. V. and Kolmogorov, A. N. (1949).Limit Distributions for Sum of Independent Random Variables, Moscow, English translation, Addison-Wesley, Cambridge, Mass., 1954.

    Google Scholar 

  4. Laha, R. G. (1961). On a class of unimodal distributions,Proc. Amer. Math. Soc.,21, 181–184.

    Article  MathSciNet  Google Scholar 

  5. Lévy, P. (1937).Théorie de l'Addition des Vatiables Aléatoires, Gauthier-Villars, Paris.

    Google Scholar 

  6. Medgyessy, P. (1967). On a new class of unimodal infinitely divisible distribution functions and related topics,Studia Sci. Math. Hungar. 2, 441–446.

    MathSciNet  Google Scholar 

  7. Ramachandran, B. and Radhakrishna Rao, C. (1968). Some results on characterizations of the normal and generalized stable laws,Sankhya,30, 125–140.

    MATH  Google Scholar 

  8. Shimizu, R. (1965). Certain class of infinitely divisible characteristic functions,Ann. Inst. Statist. Math.,17, 115–132.

    Article  MATH  MathSciNet  Google Scholar 

  9. Shimizu, R. (1968). Characteristic functions satisfying a functional equation I,Ann. Inst. Statist. Math.,20, 115–132.

    MathSciNet  Google Scholar 

  10. Shimizu, R. (1969). Characteristic functions satisfying a functional equation II,Ann. Inst. Statist. Math.,21, 391–405.

    MATH  MathSciNet  Google Scholar 

  11. Shimizu R. (1970). Corrections to characteristic functions satisfying a functional equation II,Ann. Inst. Statist. Math.,22, 185–186.

    MATH  MathSciNet  Google Scholar 

  12. Wintner, A. (1936). On a class of fourier transforms,Amer. J. Math.,58, 45–90.

    Article  MATH  MathSciNet  Google Scholar 

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The Institute of Statistical Mathematics

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Shimizu, R. On the domain of partial attraction of semi-stable distributions. Ann Inst Stat Math 22, 245–255 (1970). https://doi.org/10.1007/BF02506340

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  • DOI: https://doi.org/10.1007/BF02506340

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