Skip to main content
SpringerLink
Log in

Moderate and Large Deviation Estimate for the Markov-Binomial Distribution

  • Published:
Acta Applicandae Mathematicae Aims and scope Submit manuscript

Abstract

Considering the Markov-binomial distribution, we obtain the moderate deviation and large deviation estimates for the number of successes S n and the number of experiments Y(r) until the rth success.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Altham, P.: Two generalizations of the binomial distribution. Appl. Stat. 27, 162–167 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  2. Campbell, S.A., Godbole, A.P., Schaller, S.: Discriminating between sequences of Bernoulli and Markov–Bernoulli trials. Commun. Stat. Theory Methods 23, 2787–2814 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  3. Čekanavičius, V., Mikalauskas, M.: Signed Poisson approximations for Markov chains. Stoch. Process. Appl. 82, 205–227 (1999)

    Article  MATH  Google Scholar 

  4. Čekanavičius, V., Mikalauskas, M.: Large deviations for the Markov Binomial distribution. Lith. Math. J. 41(4), 307–318 (2001)

    Article  MATH  Google Scholar 

  5. Čekanavičius, V., Roos, B.: Binomial approximation to the Markov binomial distribution. Acta Appl. Math. 96, 137–146 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chou, T.T., Yang, C.N.: Binomial distribution for the charge asymmetry parameter. Phys. Lett. B 135(13), 175–178 (1984)

    Google Scholar 

  7. Cossette, H., Landriault, D., Marceau, É.: Ruin probabilities in the compound Markov binomial model. Scand. Actuar. J. 4, 301–323 (2003)

    Article  MathSciNet  Google Scholar 

  8. Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications, 2nd edn. Springer, New York (1998)

    MATH  Google Scholar 

  9. Dobrushin, R.L.: Limit theorems for a two-state Markov chain. Izv. Akad. Nauk USSR, Ser. Mat. 17, 291–330 (1953)

    MATH  Google Scholar 

  10. Dumitrescu, M.: Statistical inference for two Markov binomial models with applications. Stat. Pap. 43, 579–585 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Edwards, A.W.F.: The meaning of binomial distribution. Nature (London) 186, 1074 (1960)

    Article  MATH  Google Scholar 

  12. Ivchenko, G.I.: On comparison of the binomial and Poisson laws. Theor. Probab. Appl. 19, 584–587 (1974)

    Article  MATH  Google Scholar 

  13. Madsen, R.W.: Generalized binomial distributions. Commun. Stat. Theory Methods 22(11), 3065–3086 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  14. Omey, E., Santos, J., Van Gulck, S.: A Markov-binomial distribution. Appl. Anal. Discrete Math. 2(1), 38–50 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Soon, S.Y.T.: Binominal approximation for dependent indicators. Stat. Sin. 6, 703–714 (1996)

    MATH  MathSciNet  Google Scholar 

  16. Wang, Y.H.: On the limit of the Markov binomial distribution. J. Appl. Probab. 18, 937–942 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  17. Willmot, G.E.: Ruin probabilities in the compound binomial model. Insur. Math. Econ. 12, 133–142 (1993)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Zhengzhou University, Zhengzhou, Henan Province, 450052, China

    Guangyu Yang

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan Province, 453007, China

    Yu Miao

Authors
  1. Guangyu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu Miao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guangyu Yang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, G., Miao, Y. Moderate and Large Deviation Estimate for the Markov-Binomial Distribution. Acta Appl Math 110, 737–747 (2010). https://doi.org/10.1007/s10440-009-9471-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10440-009-9471-z

Keywords

Mathematics Subject Classification (2000)

Search

Navigation