On a simultaneous characterization of the poisson law and the gamma distribution

  • R R Hall
  • I Vincze
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 861)


The authors consider the following problem due to A Rényi and I Vincze: if for the entire function f(t)=1+a1t+a2t2+. ... with positive coefficients we have Open image in new window then is it necessary that f(t) ≡ et? Some results in this direction were proved in [2], [5]. Now it is shown that if 1/f is completely monotone then we must have f(t) ≡ et.


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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • R R Hall
    • 1
    • 2
  • I Vincze
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of YorkYorkEngland
  2. 2.Department of Mathematical StatisticsMathematical Institute of the Hungarian Academy of SciencesBudapest

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