Bulletin of the American Mathematical Society

MathSciNet review: 1567224
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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.

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.

M. Kac, On a characterization of the normal distribution, Amer. J. Math. 61 (1939), 726–728. MR 371, DOI 10.2307/2371328

A. M. Kagan, Yu. V. Linnik, and C. Radhakrishna Rao, Characterization problems in mathematical statistics, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York-London-Sydney, 1973. Translated from the Russian by B. Ramachandran. MR 0346969

Tatsuo Kawata and Heihati Sakamoto, On the characterisation 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, DOI 10.2969/jmsj/00120111

Yu. V. Linnik, Linear forms and statistical criteria. I, II, Ukrain. Mat. Žurnal 5 (1953), 207–243, 247–290 (Russian). MR 0060767

Eugene Lukacs, A characterization of the normal distribution, Ann. Math. Statistics 13 (1942), 91–93. MR 6626, DOI 10.1214/aoms/1177731647

J. Marcinkiewicz, Sur une propriété de la loi de Gauß, Math. Z. 44 (1939), no. 1, 612–618 (French). MR 1545791, DOI 10.1007/BF01210677

Georg Pólya, Herleitung des Gaußschen Fehlergesetzes aus einer Funktionalgleichung, Math. Z. 18 (1923), no. 1, 96–108 (German). MR 1544622, DOI 10.1007/BF01192398

V. P. Skitovič, Linear forms of independent random variables and the normal distribution law, Izvestiya Akad. Nauk SSSR. Ser. Mat. 18 (1954), 185–200 (Russian). MR 0062972

A. A. Zinger, On independent samples from normal populations, Uspehi Matem. Nauk (N.S.) 6 (1951), no. 5(45), 172–175 (Russian). MR 0044792

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 0000371

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), 612-618. MR 1545791

9.

G. Pólya, Herleitung des Gauszschen Fählergesetzes aus einer Funktionalgleichung, Math. Z. 18 (1923), 96-108. MR 1544622

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