Advances and Applications in Statistics
Volume 13, Issue 1, Pages 95 - 109
(October 2009)
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A NUMERICAL ALGORITHM FOR DISTRIBUTIONS OF SOONEST WAITING TIME PROBLEMS IN MARKOV DEPENDENT TRIALS
Bruce Chaderjian (U.S.A.), Morteza Ebneshahrashoob (U.S.A.) and Tangan Gao (U.S.A.)
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Abstract: Waiting time random variables have a wide variety of interesting and useful applications. In this paper, we study the soonest waiting time for the independent multinomial as well as first-order Markov dependent trials via conditional probability generating functions. Our model is very general and covers various models proposed by many researchers. A computer algorithm is also developed to calculate the distributions, marginal probabilities, expectations and standard deviations. Numerical results show that the algorithm is efficient and is capable of handling large problems. |
Keywords and phrases: waiting time problem, probability generating function, independent multinomial trial, first-order Markov dependent trial. |
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