On characterizing the gamma and the normal distribution.
Ignacy Kotlarski
Source: Pacific J. Math. Volume 20, Number 1
(1967), 69-76.
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Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102992970
Zentralblatt MATH identifier: 0168.17803
Mathematical Reviews number (MathSciNet): MR0203769
References
[1] I. Kotlarski, On pairs of independent random variables whose quotients follow some known distribution, Colloquium Mathematicum, Vol. IX, 1962, Fasc. 1, 151-162.
Mathematical Reviews (MathSciNet): MR24:A3730
Zentralblatt MATH: 0105.11901
[2] I. Kotlarski, On random variables whose quotient follows the Cauchy law, Colloquium Mathematicum, Vol. VII, 1960, Fasc. 2, 278-284.
Mathematical Reviews (MathSciNet): MR22:9998
Zentralblatt MATH: 0093.15101
[3] R. G. Laha, An example of a non-normal distribution where the quotient follows the Cauchy law, Proceedings of the National Academy of Sciences 44 (1958),222-223. 4#fOn a class of distribution functions where the quotient follows the Cauchy law, Transactions of the American Mathematical Society 93 (1959), 205-215. 5.1On the laws of Cauchy and Gauss, Ann. Math. Statist. 30 (1959) 1165-1174.
[6] R. G. Laha, On a problem connected with beta and gamma distributions, Transactions of the American Mathematical Society, Vol. 113, No. 2, November 1964, 287-298.
Mathematical Reviews (MathSciNet): MR30:1528
Zentralblatt MATH: 0138.41105
[7] E. Lukacs and R. G. Laha, Application of Characteristic Functions, London, 1964.
Mathematical Reviews (MathSciNet): MR30:2582
Zentralblatt MATH: 0117.36402
[8] A. J. Markushevitsh, Teoria analititsheskich funkcji,Moskwa, 1950, (The Theory of Analytical Functions, Moskow, 1950, Russian).
[9] J. G. Mauldon, Characterizingproperties of statisticaldistributions,Quarterly Journal of Mathematics, Oxford Series, 2.7, 1956, 155-160.
Mathematical Reviews (MathSciNet): MR20:4884
Zentralblatt MATH: 0074.14401
[10] G. P. Steck, A uniqueness property not enjoyed by the normal distribution, Ann. Math. Statist. 29 (1958) 604-606.
Mathematical Reviews (MathSciNet): MR20:4901
Zentralblatt MATH: 0086.34203
Pacific Journal of Mathematics
