Binomial approximation to the Poisson binomial distribution: The Krawtchouk expansion

Theory of Probability and its Applications

Volumn 45, Issue 2, 2001, Pages 258-272

  Roos, B ^a  

^a UNIVERSITY OF HAMBURG   (Germany)

Author keywords

Binomial approximation; Krawtchouk expansion; Point metric; Poisson binomial distribution; Signed measures; Total variation distance

Indexed keywords

EID: 0035648910     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0040585X9797821X     Document Type: Article

References (23)

1. A. D. BARBOUR, L. HOLST, AND S. JANSON, Poisson Approximation, Clarendon Press, Oxford, 1992.
2. P. DEHEUVELS AND D. PFEIFER, A semigroup approach to Poisson approximation, Ann. Probab., 14 (1986), pp. 663-676.
3. P. DEHEUVELS AND D. PFEIFER, On a relationship between Uspensky's theorem and Poisson approximations, Ann. Inst. Statist. Math., 40 (1988), pp. 671-681.
4. P. DEHEUVELS, D. PFEIFER, AND M. L. PURI, A new semigroup technique in Poisson approximation, Semigroup Forum, 38 (1989), pp. 189-201.
5. P. DEHEUVELS, M. L. PURI, AND S. S. RALESCU, Asymptotic expansions for sums of nonidentically distributed Bernoulli random variables, J. Multivariate Anal., 28 (1989), pp. 282-303.
6. W. FELLER, An Introduction to Probability Theory and Its Applications, I. Wiley, New York, 1968.
7. P. FRANKEN, Approximation der Verteilungen von Summen unabhängiger nichtnegativer ganzzahliger Zufallsgrößen durch Poissonsche Verteilungen, Math. Nachr., 27 (1964), pp. 303-340.
8. W. EHM, Binomial approximation to the Poisson binomial distribution, Statist. Probab. Lett., 11 (1991), pp. 7-16.
9. Š. JAKŠEVIČIUS, Approximation by a binomial type law, Lithuanian Math. J., 32 (1992), pp. 174-180.
10. L. LE CAM, An approximation theorem for the Poisson binomial distribution, Pacific J. Math., 10 (1960), pp. 1181-1197.
11. W.-L. LOH, Stein's method and multinomial approximation, Ann. Appl. Probab., 2 (1992), pp. 536-554.
12. H. MAKABE, On approximations to some limiting distributions with applications to the theory of sampling inspections by attributes, Kodai Math. Semin. Rep., 16 (1964), pp. 1-17.
13. V. G. MIKHAILOV, On a refinement of the central limit theorem for sums of independent random indicators, Theory Probab. Appl., 38 (1993), pp. 479-489.
14. Y. V. PROKHOROV, Asymptotic behaviour of the binomial distribution, Select. Transl. Math. Statist. and Probab., 1 (1961), pp. 87-95.
15. A. RÉNYI, Probability Theory, North-Holland, Amsterdam, 1970.
16. B. ROOS, A semigroup approach to Poisson approximation with respect to the point metric, Statist. Probab. Lett., 24 (1995), pp. 305-314.
17. B. ROOS, Asymptotics and sharp bounds in the Poisson approximation to the Poisson binomial distribution, Bernoulli, 5 (1999), pp. 1021-1034.
18. S. YA. SHORGIN, Approximation of a generalized binomial distribution, Theory Probab. Appl., 22 (1977), pp. 846-850.
19. S. Y. T. SOON, Binomial approximation for dependent indicators, Statist. Sinica, 6 (1996), pp. 703-714.
20. G. SZEGÖ, Orthogonal Polynomials, AMS, Providence, RI, 1975.
21. K. TAKEUCHI AND A. TAKEMURA, On sum of 0-1 random variables. I. Univariate case, Ann. Inst. Statist. Math., 39 (1987), pp. 85-102.
22. J. V. USPENSKY, Introduction to Mathematical Probability, McGraw-Hill, New York, 1937.
23. A. YU. VOLKOVA, A refinement of the central limit theorem for sums of independent random indicators, Theory Probab. Appl., 40 (1995), pp. 791-794.