The asymptotic normality of certain combinatorial distributions

  • Ch. A. Charalambides


The numbersC(m, n, s) and |C(m, n, −s)|,s>0, appearing in then-fold convolution of truncated binomial and negative binomial distributions, respectively, are shown to be asymptotically normal. Moreover a concavity property for these numbers is concluded.


Asymptotic Formula Asymptotic Normality Negative Binomial Distribution Stirling Number Maclaurin Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Cacoullos, T. and Charalambides Ch. (1975). On minimum variance unbiased estimation for truncated binomial and negative binomial distributions,Ann. Inst. Statist. Math.,27, 235–244.MathSciNetGoogle Scholar
  2. [2]
    Charalambides, Ch. (1972). A new kind of numbers appearing in then-fold convolution of truncated binomial and negative binomial distributions, submitted for publication to theJ. Comb. Theory.Google Scholar
  3. [3]
    Feller, W. (1968).An Introduction to Probability Theory and Its Applications, Vol. 1 (3rd ed.) Wiley, New York.MATHGoogle Scholar
  4. [4]
    Gončarov, V. (1944) Du domaine d'analyse combinatoroire,Bull. Acad. Sci. U.S.S.R., Ser. Math.,8, 3–48 (in Russian with French summary).Google Scholar
  5. [5]
    Haigh, J., (1972). Random equivalence relations,J. Comb. Theory, Ser. A,13, 287–295.CrossRefMathSciNetGoogle Scholar
  6. [6]
    Hardy, Littlewood and Polya (1959).Inequalities, 2nd ed., Cambridge Univ. Press, Cambridge, England, pp. 104–105 and pp. 51–54.Google Scholar
  7. [7]
    Harper, L. H. (1967). Stirling behavior is asymptotically normal,Ann. Math. Statist.,38, 410–414.MathSciNetGoogle Scholar
  8. [8]
    Loève, M. (1960).Probability Theory, 2nd ed., Van Nostrand, Princeton.MATHGoogle Scholar
  9. [9]
    Moser, L., and Wyman, M. (1955). An asymptotic formula for the Bell numbers,Trans. Roy. Soc. Canada,49, 49–53.MathSciNetGoogle Scholar
  10. [10]
    Szekeres, G. and Binet, F. E. (1957). On Borel fields over finite sets,Ann. Math. Statist.,28, 494–498.MathSciNetGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics 1976

Authors and Affiliations

  • Ch. A. Charalambides
    • 1
  1. 1.University of AthensAthensGreece

Personalised recommendations