Distributions of Patterns of Pair of Successes Separated by Failure Runs of Length at Least k1 and at Most k2 Involving Markov Dependent Trials : GERT Approach

الملخص EN

We use the Graphical Evaluation and Review Technique (GERT) to obtain probability generating functions of the waiting time distributions of 1st, and mth nonoverlapping and overlapping occurrences of the pattern Λfk1,k2=SFF⋯F︸k1≤kf≤k2S (k1>0), involving homogenous Markov dependent trials.

GERT besides providing visual picture of the system helps to analyze the system in a less inductive manner.

Mean and variance of the waiting times of the occurrence of the patterns have also been obtained.

Some earlier results existing in literature have been shown to be particular cases of these results.