DERIVATION OF THE PROBABILITY DISTRIBUTION FUNCTIONS FOR SUCCESSION QUOTA RANDOM VARIABLES

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

1Department of Economics, University of Crete, Perivolia-Rethimno 74100, Greece 2Department of Mathematics, University of Patras, Patras 26110, Greece

(Received August 22, 1994; revised September 26, 1995)

Abstract. The probability distribution functions (pdf’s) of the sooner and later waiting time random variables (rv’s) for the succession quota problem (k successes and r failures) are derived presently in the case of a binary sequence of order k. The probability generating functions (pgf’s) of the above rv’s are then obtained directly from their pdf’s. In the case of independent Bernoulli trials, expressions for the pdf’s in terms of binomial coefficients are also established.

Key words and phrases: Succession quota, sooner and later problems, Bernoulli trials, binary sequence of order k, probability distribution function, probability generating function, longest run.