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Discrete distributions of orderk on a binary sequence

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Summary

This paper considers discrete distributions of orderk based on a binary sequence which is defined as an extension of independent trials with a constant success probability and is more practical than the independent trials. Some results on calculation of probabilities and characteristics of the distributions are obtained as well as their formal expressions. Examples and an application are also given.

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References

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Chiang, D. and Niu, S. C. (1981). Reliability of consecutive-k-out-of-n:F system,IEEE Transactions on Reliability,R-30, April, 87–89.

    Article  Google Scholar 

  4. Derman, C., Lieberman, G. J. and Ross, S. M. (1982). On the consequtive-k-ofn:F system,IEEE Transactions on Reliability,R-31, April, 57–63.

    Article  Google Scholar 

  5. Feller, W. (1968).An Introduction to Probability Theory and its Applications, vol. I (3rd edn.), John Wiley and Sons, Inc., New York.

    MATH  Google Scholar 

  6. Fishier, R. A., Corbet, A. S. and Williams, C. B. (1943). The relation between the number of species and the number of individuals in a random sample of an animal population,Journal of Animal Ecology,12, 42–57.

    Article  Google Scholar 

  7. Hirano, K. (1984). Some properties of the distributions of orderk, to appear inProceedings of the First International Conference on Fibonacci Numbers and Their Applications (1984), edited by A. N. Philippou and A. F. Horadam, Gutenberg, Athens.

  8. Johnson, N. L. and Kotz, S. (1969).Distributions in Statistics: Discrete Distributions, John Wiley and Sons, Inc., New York.

    MATH  Google Scholar 

  9. Philippou, A. N. (1983). The Poisson and compound Poisson distributions of orderk and some of their properties,Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V.A. Steklova AN SSSR,130, 175–180, (Russian, English summary).

    MATH  Google Scholar 

  10. Philippou, A. N., Georghiou, C. and Philippou, G. N. (1983). A generalized geometric distribution and some of its properties,Statistics and Probability Letters,1, 171–175.

    Article  MathSciNet  Google Scholar 

  11. Philippou, A. N. and Muwafi, A. A. (1982). Waiting for thekth consecutive success and the Fibonacci sequence of orderk, The Fibonacci Quarterly,20, 28–32.

    MathSciNet  MATH  Google Scholar 

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Authors
  1. Sigeo Aki
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The Institute of Statistical Mathematics

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Aki, S. Discrete distributions of orderk on a binary sequence. Ann Inst Stat Math 37, 205–224 (1985). https://doi.org/10.1007/BF02481092

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  • DOI: https://doi.org/10.1007/BF02481092

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