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Non uniform exponential bounds on normal approximation by Stein’s method and monotone size bias couplings

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  • Kamonrat Kamjornkittikoon
  • Kritsana Neammanee
  • Nattakarn Chaidee

Abstract

It is known that the normal approximation is applicable for sums of non negative random variables, W, with the commonly employed couplings. In this work, we use the Stein’s method to obtain a general theorem of non uniform exponential bound on normal approximation base on monotone size bias couplings of W. Applications of the main result to give the bound on normal approximation for binomial random variable, the number of bulbs on at the terminal time in the lightbulb process, and the number of m runs are also provided.

Suggested Citation

  • Kamonrat Kamjornkittikoon & Kritsana Neammanee & Nattakarn Chaidee, 2018. "Non uniform exponential bounds on normal approximation by Stein’s method and monotone size bias couplings," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(5), pages 1117-1132, March.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:5:p:1117-1132
    DOI: 10.1080/03610926.2017.1316404
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