A Markov-binomial distribution

Edward Omey (), J. Santos () and Stefan Van Gulck ()
Additional contact information
Edward Omey: Hogeschool-Universiteit Brussel (HUB), Belgium
J. Santos: Public University of Navarre, Pamplona, Spain
Stefan Van Gulck: Hogeschool-Universiteit Brussel (HUB), Belgium

No 2007/15, Working Papers from Hogeschool-Universiteit Brussel, Faculteit Economie en Management

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.

Keywords: Markov chain; generalized binomial distribution; central limit theorem (search for similar items in EconPapers)
Pages: 16 pages
Date: 2007-09
References: Add references at CitEc
Citations:

Downloads: (external link)
http://lirias.hubrussel.be/handle/123456789/2189 (application/pdf)
Our link check indicates that this URL is bad, the error code is: 500 Can't connect to lirias.hubrussel.be:80 (nodename nor servname provided, or not known)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hub:wpecon:200715

Access Statistics for this paper

More papers in Working Papers from Hogeschool-Universiteit Brussel, Faculteit Economie en Management Contact information at EDIRC.
Bibliographic data for series maintained by Sabine Janssens ( this e-mail address is bad, please contact ).