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SUCCESS RUNS OF LENGTH *k* IN

MARKOV DEPENDENT TRIALS

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S. G. MOHANTY

*Department of Mathematics and Statistics, McMaster University,*

Hamilton, Ontario, Canada L8S 4K1
(Received June 16, 1993; revised December 9, 1993)

**Abstract.**
The geometric type and inverse
Polýa-Eggenberger type distributions of waiting time for success
runs of length *k* in two-state Markov dependent trials are
derived by using the probability generating function method and
the combinatorial method. The second is related to the minimal
sufficient partition of the sample space. The first two moments
of the geometric type distribution are obtained. Generalizations
to ballot type probabilities of which negative binomial
probabilities are special cases are considered. Since the
probabilities do not form a proper distribution, a modification
is introduced and new distributions of order *k* for Markov
dependent trials are developed.

*Key words and phrases*:
Ballot problem, success
runs, Markov dependent trials, discrete distributions.

**Source**
( TeX ,
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