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Poisson and compound Poisson distributions of order k and some of their properties

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Abstract

One investigates the Poisson distribution of orderk. One finds its generating function and with its aid one establishes that the sum of independent random variables, distributed according to the Poisson law of orderk, is distributed in the same manner. In addition, one considers a generalized compound Poisson distribution.

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Literature cited

  1. A. N. Philippou, “The negative binomial distribution of orderk and some of its properties,” Biometrical J.,25 (1983).

  2. A. N. Philippou, C. Georghiou, and G. N. Philippou, “A generalized geometric distribution and some of its properties,” Probab. Statist. Lett.,11 (1983).

  3. A. M. Mood, F. A. Graybill, and D. C. Boes, Introduction to the Theory of Statistics, McGraw-Hill, New York (1974).

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  4. D. A. Raikov, “On the expansions of the Gauss and Poisson laws,” Izv. Akad. Nauk SSSR, Ser. Mat.,2, No. 1, 91–124 (1938).

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Authors
  1. N. Andreas Filippu
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 175–180, 1983.

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Filippu, N.A. Poisson and compound Poisson distributions of order k and some of their properties. J Math Sci 27, 3294–3297 (1984). https://doi.org/10.1007/BF01850680

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  • DOI: https://doi.org/10.1007/BF01850680

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