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

Affiliation(s)

Department of Mathematics and Statistics, California State University, Long Beach, USA.

Department of Mathematics and Statistics, California State University, Long Beach, USA.

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.

We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve

Cite this paper

B. Chaderjian, M. Ebneshahrashoob and T. Gao, "Exact Distributions of Waiting Time Problems of Mixed Frequencies and Runs in Markov Dependent Trials,"*Applied Mathematics*, Vol. 3 No. 11, 2012, pp. 1689-1696. doi: 10.4236/am.2012.311234.

B. Chaderjian, M. Ebneshahrashoob and T. Gao, "Exact Distributions of Waiting Time Problems of Mixed Frequencies and Runs in Markov Dependent Trials,"

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