On Convergence Rates in the Central Limit Theorems for Combinatorial Structures

@article{Hwang1998OnCR,
  title={On Convergence Rates in the Central Limit Theorems for Combinatorial Structures},
  author={Hsien-Kuei Hwang},
  journal={Eur. J. Comb.},
  year={1998},
  volume={19},
  pages={329-343}
}
Flajolet and Soria established several central limit theorems for the parameter “number of components” in a wide class of combinatorial structures. In this paper, we shall prove a simple theorem which applies to characterize the convergence rates in their central limit theorems. This theorem is also applicable to arithmetical functions. Moreover, asymptotic expressions are derived for moments of integral order. Many examples from different applications are discussed. 

From This Paper

Topics from this paper.
91 Citations
30 References
Similar Papers

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 30 references

Stirling behaviour is asymptotically normal

  • L. H. Harper
  • Annals of Mathematical Statistics,
  • 1967
Highly Influential
3 Excerpts

On asymptotic expansions in the central and local limit theorems for combinatorial structures

  • J. Knopfmacher Knopfmacher, R. Warlimont
  • Théorèmes limites pour les structures…
  • 1994

Théorèmes limites pour les structures combinatoires et les fonctions arithmétiques, Thèse

  • H.-K. Hwang
  • Ecole polytechnique,
  • 1994
2 Excerpts

Factorisatio numerorum” in arithmetical semigroups

  • A. Knopfmacher, J. Knopfmacher, R. Warlimont
  • Acta Arithmetica,
  • 1992
1 Excerpt

A local limit theorem for generalized Stirling numbers

  • A. Ruciński, B. Voigt
  • Revue Roumaine de Mathématiques Pures et…
  • 1990

Similar Papers

Loading similar papers…