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A Markov-binomial distribution

Author

Listed:
  • Omey, Edward

    (Hogeschool-Universiteit Brussel (HUB), Belgium)

  • Santos, J.

    (Public University of Navarre, Pamplona, Spain)

  • Van Gulck, Stefan

    (Hogeschool-Universiteit Brussel (HUB), Belgium)

Abstract

Let fXi; i _ 1g denote a sequence of f0; 1g-variables and suppose that the sequence forms a Markov Chain. In the paper we study the number of successes Sn = X1 + X2 + ::: + Xn and we study the number of experiments Y (r) up to the rth success. In the i.i.d. case Sn has a binomial distribution and Y (r) has a negative binomial distribution and the asymptotic behaviour is well known. In the more generalMarkov chain case, we prove a central limit theorem for Sn and provide conditions under which the distribution of Sn can be approximated by a Poisson-type of distribution. We also completely characterize Y (r) and show that Y (r) can be interpreted as the sum of r independent r.v. related to a geometric distribution.

Suggested Citation

  • Omey, Edward & Santos, J. & Van Gulck, Stefan, 2007. "A Markov-binomial distribution," Working Papers 2007/15, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    • Handle: RePEc:hub:wpecon:200715
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    File URL: http://lirias.hubrussel.be/handle/123456789/2189
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