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On multiparameter distributions of order k

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Abstract

A multiparameter negative binomial distribution of order k is obtained by compounding the extended (or multiparameter) Poisson distribution of order k by the gamma distribution. A multiparameter logarithmic series distribution of order k is derived next, as the zero truncated limit of the first distribution. Finally a few genesis schemes and interrelationships are established for these three multiparameter distributions of order k. The present work extends several properties of distributions of order k.

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References

  • Adelson R. M. (1966). Compound Poisson distributions, Operational Research Quarterly, 17, 73–75.

    Article  Google Scholar 

  • Aki S. (1985). Discrete distributions of order k on a binary sequence, Ann. Inst. Statist. Math., 37, 205–224.

    Article  MathSciNet  Google Scholar 

  • Aki S., Kuboki H. and Hirano K. (1984). On discrete distributions of order k, Ann. Inst. Statist. Math., 36, 431–440.

    Article  MathSciNet  Google Scholar 

  • Charalambides Ch. A. (1986). On discrete distributions of order k, Ann. Inst. Statist. Math., 38, 557–568.

    Article  MathSciNet  Google Scholar 

  • Hirano K. (1986). Some properties of the distributions of order k, Fibonacci Numbers and Their Applications: Proceedings of the First International Conference on Fibonacci Numbers and Their Applications (Patras 1984), (eds. A. N. Philippou, G. E. Bergum and A. F. Horadam), 45–53, Reidel, Dordrecht.

    Google Scholar 

  • Johnson N. L. and Kotz S. (1969). Discrete distributions, Houghton-Mifflin, New York.

    MATH  Google Scholar 

  • Philippou A. N. (1983). Poisson and compound Poisson distributions of order k and some of their properties, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov., 130, 175–180 (in Russian, English summary).

    MATH  Google Scholar 

  • Philippou A. N. (1984). The negative binomial distribution of order k and some of its properties, Biometrical J., 26, 789–794.

    Article  MathSciNet  Google Scholar 

  • Philippou A. N., Georghiou C. and Philippou G. N. (1983). A generalized goemetric distribution and some of its properties, Statist. Probab. Lett., 1, 171–175.

    Article  MathSciNet  Google Scholar 

  • Philippou A. N. and Makri F. S. (1986). Successes, runs and longest runs, Statist. Probab. Lett., 4, 211–215.

    Article  MathSciNet  Google Scholar 

  • Philippou A. N. and Muwafi A. A. (1982). Waiting for the kth consecutive success and the Fibonacci sequence of order k, Fibonacci Quart., 20, 28–32.

    MathSciNet  MATH  Google Scholar 

  • Xekalaki E., Panaretos J. and Philippou A. N. (1987). On some mixtures of distributions of order k, Fibonacci Quart., 25, 151–160.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Patras, Patras, Greece

    Andreas N. Philippou

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  1. Andreas N. Philippou
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Philippou, A.N. On multiparameter distributions of order k . Ann Inst Stat Math 40, 467–475 (1988). https://doi.org/10.1007/BF00053059

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  • DOI: https://doi.org/10.1007/BF00053059

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