On generalized binomial and multinomial distributions and their relation to generalized Poisson distributions

  • John Panaretos
  • Evdokia Xekalaki


The binomial and multinomial distributions are, probably, the best known distributions because of their vast number of applications. The present paper examines some generalizations of these distributions with many practical applications. Properties of these generalizations are studied and models giving rise to them are developed. Finally, their relationship to generalized Poisson distributions is examined and limiting cases are given.

Key words

Cluster binomial distribution cluster multinomial distribution generalized Poisson distribution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Aki, S., Kuboki, H. and Hirano, K. (1984). On discrete distributions of orderk, Ann. Inst. Statist. Math.,36, 431–440.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Charalambides, Ch. A. (1977). On the generalized discrete distributions and the Bell polynomials.Sankhyã, B,39, 36–44.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Feller, W. (1970).An Introduction to Probability Theory and Its Applications, (Revised printing of the third edition), Wiley, New York.zbMATHGoogle Scholar
  4. [4]
    Panaretos, J. and Xekalaki, E. (1984). Definition and properties of a generalized binomial distribution,Technical Report No. 1 (June 1984), Department of Mathematics, University of Crete, Greece.zbMATHGoogle Scholar
  5. [5]
    Steyn, H. S. (1956). On the univariable seriesF(t)=F(a; b1,b2...,bk;c; t, t2, ...,tk) and its application in probability theory,Proc. Kon. Ned. Akad. V. Wetensch., Ser. A,59, 190–197.Google Scholar
  6. [6]
    Steyn, H. S. (1963). On approximations for the discrete distributions obtained from multiple events,Proc. Kon. Ned. Akad. V. Wetensch., Series A,66, 85–96.MathSciNetzbMATHGoogle Scholar
  7. [7]
    Xekalaki, E. and Pararetos, J. (1983). Identifiability of compound Poisson distributions,Scand. Actuarial J.,1983, 39–45.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1986

Authors and Affiliations

  • John Panaretos
    • 1
    • 2
  • Evdokia Xekalaki
    • 1
    • 2
  1. 1.University of PatrasGreece
  2. 2.Athens School of EconomicsUniversity of CreteGreece

Personalised recommendations