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Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Janos Galambos and Samuel Kotz
Title: Characterizations of probability distributions
Additional book information: Lecture Notes in Math., vol. 675, Springer-Verlag, Berlin-Heidelberg-New York, 1978, viii + 169 pp., $9.80.

References [Enhancements On Off] (What's this?)

  • 1. S. N. Bernstein, Sur une propriété caractéristique de la loi de Gauss, Trans. Leningrad Polytechn. Inst. 3 (1941), 21-22.
  • 2. R. C. Geary, Distribution of "Student's" ratio for non-normal samples, J. Roy. Statist. Soc. Ser. B 3 (1936), 178-184.
  • 3. M. Kac, On a characterization of the normal distribution, Amer. J. Math. 61 (1939), 726-728. MR 371
  • 4. A. M. Kagan, Yu. V. Linnik and C. R. Rao, Characterization problems in mathematical statistics (translated from the Russian text by B. Ramachandran), John Wiley and Sons, New York, 1973. MR 346969
  • 5. T. Kawata and H. Sakamato, On the characterization of the normal population by the independence of the sample mean and the sample variance, J. Math. Soc. Japan 1 (1949), 111-115. MR 31672
  • 6. Yu. V. Linnik, Linear forms and statistical criteria, I, II, Ukrain. Mat. Ž. 5 (1953), 207-243; 247-290; (Selected Translations in Mathematical Statistics and Probability, 3, 1-40; 41-90.) MR 60767
  • 7. E. Lukacs, A characterization of the normal distribution, Ann. Math. Statist. 13 (1942), 91-93. MR 6626
  • 8. J. Marcinkiewicz, Sur une propriété de la loi de Gauß, Math. Z. 44 (1939), no. 1, 612–618 (French). MR 1545791, https://doi.org/10.1007/BF01210677
  • 9. Georg Pólya, Herleitung des Gaußschen Fehlergesetzes aus einer Funktionalgleichung, Math. Z. 18 (1923), no. 1, 96–108 (German). MR 1544622, https://doi.org/10.1007/BF01192398
  • 10. V. P. Skitovič, Linear forms in independent random variables and the normal distribution law, Izv. Akad. Nauk SSSR Ser. Mat. 18 (1954), 185-200 (Russian). MR 62972
  • 11. A. Zinger, On independent samples from a normal population, Uspehi Mat. Nauk 6 (1951), 172-175 (Russian). MR 44792

Review Information:

Reviewer: S. G. Ghurye
Journal: Bull. Amer. Math. Soc. 2 (1980), 256-259
DOI: https://doi.org/10.1090/S0273-0979-1980-14742-4
American Mathematical Society