Skip to main content
Log in

On discrete distributions of orderk

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

This paper gives some results on calculation of probabilities and moments of the discrete distributions of orderk. Further, a new distribution of orderk, which is called the logarithmic series distribution of orderk, is investigated. Finally, we discuss the meaning of theorder of the distributions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Feller, W. (1968).An Introduction to Probability Theory and its Applications, Vol. I (3rd ed.), John Wiley and Sons, New York.

    MATH  Google Scholar 

  3. Fisher, 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 

  4. Hirano, K., Kuboki, H., Aki, S. and Kuribayashi, A. (1984). Figures of probability density functions in statistics II—discrete univariate case—,Computer Science Monographys, No.20, The Institute of Statistical Mathematics, Tokyo.

    Google Scholar 

  5. Philippou, A. N. (1984). The Poisson and compound Poisson distribution of orderk and some of their properties,Zapiski Nauchnyka Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im, V. A. Steklova AN SSSR,130, 175–180.

    Google Scholar 

  6. 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 

  7. 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 

Download references

Authors

Additional information

The Institute of Statistical Mathematics

About this article

Cite this article

Aki, S., Kuboki, H. & Hirano, K. On discrete distributions of orderk . Ann Inst Stat Math 36, 431–440 (1984). https://doi.org/10.1007/BF02481981

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02481981

Key words

Navigation