Pacific Journal of Mathematics

On characterizing the gamma and the normal distribution.

Ignacy Kotlarski

Article information

Source
Pacific J. Math., Volume 20, Number 1 (1967), 69-76.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102992970

Mathematical Reviews number (MathSciNet)
MR0203769

Zentralblatt MATH identifier
0168.17803

Subjects
Primary: 60.20
Secondary: 62.10

Citation

Kotlarski, Ignacy. On characterizing the gamma and the normal distribution. Pacific J. Math. 20 (1967), no. 1, 69--76. https://projecteuclid.org/euclid.pjm/1102992970


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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.
  • [2] I. Kotlarski, On random variables whose quotient follows the Cauchy law, Colloquium Mathematicum, Vol. VII, 1960, Fasc. 2, 278-284.
  • [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.
  • [7] E. Lukacs and R. G. Laha, Application of Characteristic Functions, London, 1964.
  • [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.
  • [10] G. P. Steck, A uniqueness property not enjoyed by the normal distribution, Ann. Math. Statist. 29 (1958) 604-606.