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

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Analytical Methods in Probability Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 861))

Abstract

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 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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References

  1. Freud, G., Restglied eines Teuberschen Satzes I, Acta Math. Acad. Sci. Hungar., 2 (1951) 299–308.

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  2. Hall, R.R. and Williamson, J.H., On a certain functional equation, J. London Math. Soc., 12 (1976), 133–136.

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  4. Hayman, W.K., Research problems in function theory, Athlone, London, 1967.

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  5. Hayman, W.K. and Vincze, I., A problem on entire functions, Complex Analysis and its Applications, dedicated to I.N. Vekua on his 70th birthday. Izd. Nauka, Moskow 1978, 191–194.

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  6. Rényi, A., On a new axiomatic theory of probability, Acta Math. Acad. Sci. Hungar., 6 (1965) 185–335.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of York, YO1 5DD, York, England

    R R Hall & I Vincze

  2. Department of Mathematical Statistics, Mathematical Institute of the Hungarian Academy of Sciences, Budapest

    R R Hall & I Vincze

Authors
  1. R R Hall
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  2. I Vincze
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Editor information

Daniel Dugué Eugene Lukacs Vijay K. Rohatgi

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© 1981 Springer-Verlag

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Hall, R.R., Vincze, I. (1981). On a simultaneous characterization of the poisson law and the gamma distribution. In: Dugué, D., Lukacs, E., Rohatgi, V.K. (eds) Analytical Methods in Probability Theory. Lecture Notes in Mathematics, vol 861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097313

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  • DOI: https://doi.org/10.1007/BFb0097313

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10823-8

  • Online ISBN: 978-3-540-36785-7

  • eBook Packages: Springer Book Archive

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