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S. Aki and K. Hirano, “Sooner and Later Waiting Time Problems for Runs in Markov Dependent Bivariate Trials,” Annals of the Institute of Statistical Mathematics, Vol. 51, No. 1, 1999, pp. 17-29. doi:10.1023/A:1003874900507

has been cited by the following article:

• TITLE: Exact Distributions of Waiting Time Problems of Mixed Frequencies and Runs in Markov Dependent Trials

  AUTHORS: Bruce J. Chaderjian, Morteza Ebneshahrashoob, Tangan Gao

  KEYWORDS: Inverse Sampling; Multinomial Stopping Problem; Soonest through Latest Waiting Time Variable; Probability Generating Function; First-Order Markov Dependent Trial

  JOURNAL NAME: Applied Mathematics, Vol.3 No.11, November 20, 2012

  ABSTRACT: We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional γ slack cells without quotas. For any given and , in our Model I we determine the waiting time until at least frequency cells and at least run cells reach their quotas. For any given τ ≤ α + β, in our Model II we determine the waiting time until τ cells reach their quotas. Computer algorithms are developed to calculate the distributions, expectations and standard deviations of the waiting time random variables of the two models. Numerical results demonstrate the efficiency of the algorithms.