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PROBABILITY DISTRIBUTION FUNCTIONS OF SUCCESSION

QUOTAS IN THE CASE OF MARKOV DEPENDENT TRIALS

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DEMETRIOS L. ANTZOULAKOS^{1}
AND ANDREAS N. PHILIPPOU^{2}

^{1} *Department of Economics, University of Crete, Rethimno 74100, Greece*

^{2} *Department of Mathematics, University of Patras, Patras 26100, Greece*
(Received February 1, 1996; revised June 10, 1996)

**Abstract.**
The exact probability distribution functions
(pdf's) of the sooner and later waiting time random variables
(rv's) for the succession quota problem are derived presently in
the case of Markov dependent trials. This is done by means of
combinatorial arguments. The probability generating functions
(pgf's) of these rv's are then obtained by means of enumerating
generating functions (enumerators). Obvious modifications of the
proofs provide analogous results for the occurrence of frequency
quotas and such a result is established regarding the pdf of a
frequency and succession quotas rv. Longest success and failure
runs are also considered and their joint cumulative distribution
function (cdf) is obtained.

*Key words and phrases*:
Sooner and later problems,
frequency quota, succession quota, Markov dependent trials,
probability distribution function, probability generating
function, cumulative distribution function, binomial expressions,
longest run, enumerator.

**Source**
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