Pacific Journal of Mathematics

An approximation theorem for the Poisson binomial distribution.

Lucien Le Cam

Article information

Source
Pacific J. Math. Volume 10, Number 4 (1960), 1181-1197.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
http://projecteuclid.org/euclid.pjm/1103038058

Zentralblatt MATH identifier
0118.33601

Mathematical Reviews number (MathSciNet)
MR0142174

Subjects
Primary: 62.15
Secondary: 60.30

Citation

Le Cam, Lucien. An approximation theorem for the Poisson binomial distribution. Pacific J. Math. 10 (1960), no. 4, 1181--1197. http://projecteuclid.org/euclid.pjm/1103038058.


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References

  • [1] W. Doeblin, Sur les sommes d'un grand nombre de variables aleatoires indpendantes, Bull, des Sciences Mathematiques, 53, Paris (1939), 23-32.
  • [2] Nelson Dunford and Jacob T. Schwartz, Linear operators, Part I. General theory, In- terscience Publishers, New York, 1958.
  • [3] Einar Hille and Ralph S. Phillips, Functional analysis and semi groups, Amer. Math- Soc. Coll. Publ. 31, Providence, R. I. 1957.
  • [4] J. L. Hodges, Jr. and Lucien Le Cam, The Poisson approximationto the Poisson
  • [5] A. Khintchine, Asymptotische Gesetze der Wahrscheinlichkeitsrechnung, Ergebnisse der Mathematik und ihrer grenzgebiete, Julius Springer, Berlin, 1933.
  • [6] A. N. Kolmogorov, Deux theoremes asymptotiques pour les sommes de variables alatoires (Russian, French summary), Teoriia Veroiatnosteii, 1 (4), Moscow (1956), 426-436.
  • [7] Paul Levy, Theorie de addition des variables aleatoires, Gauthier-Villars, Paris, 1937.
  • [8] M. A. Naimark, Normed rings, Moscow, 1956.
  • [9] Yu. V. Prohorov, Asymptotic behavior of the binomial distribution (Russian), Uspekhii Matematicheskiikh Nauk, 8 (3), Moscow (1953), 135-142.