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ArticleOriginal scientific text

Title

A note on Poisson approximation by w-functions

Authors 1

Affiliations

  1. Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4 , 50-384 Wrocław, Poland

Abstract

One more method of Poisson approximation is presented and illustrated with examples concerning binomial, negative binomial and hypergeometric distributions.

Keywords

ENG
w-functions, Poisson, binomial, total variation distance, Stein-Chen identity, hypergeometric distributions, negative binomial

Bibliography

  1. A. D. Barbour and G. K. Eagleson (1983), Poisson approximation for some statistics based on exchangeable trials, Adv. Appl. Probab. 15, 585-560.
  2. A. D. Barbour, L. Holst and S. Janson (1992), Poisson Approximation, Oxford Univ. Press, Oxford.
  3. P. Billingsley (1979), Probability and Measure, Wiley, New York.
  4. T. Cacoullos and V. Papathanasiou (1989), Characterizations of distributions by variance bounds, Statist. Probab. Lett. 7, 351-356.
  5. T. Cacoullos, V. Papathanasiou and S. A. Utev (1994), Variational inequalities with examples and an application to the Central Limit Theorem, Ann. Probab. 22, 1607-1618.
  6. V. Papathanasiou and S. A. Utev (1995), Integro-differential inequalities and the Poisson approximation, Siberian Adv. Math. 5, 120-132.
  7. V. Veervat (1969), Upper bounds for the distance in total variation between the binomial and negative binomial and the Poisson distribution, Statist. Neerlandica 23, 79-86.
Applicationes Mathematicae
1998-1999/25/3
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Pages:
387-392
Main language of publication
English
Received
1997-12-29
Published
1998
Exact and natural sciences