Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials

1996 ◽  
Vol 48 (4) ◽  
pp. 773-787 ◽  
Author(s):  
S. Aki ◽  
N. Balakrishnan ◽  
S. G. Mohanty
Keyword(s):  
Waiting Time ◽  
Higher Order ◽  
Markov Dependent Trials

Sooner and later waiting time problems for patterns in Markov dependent trials

2003 ◽  
Vol 40 (1) ◽  
pp. 73-86 ◽  
Author(s):  
Qing Han ◽  
Katuomi Hirano
Keyword(s):  
Waiting Time ◽  
Generating Functions ◽  
Random Variables ◽  
Probability Functions ◽  
Probability Generating Functions ◽  
Markov Dependent Trials

In this paper, we investigate sooner and later waiting time problems for patterns S0 and S1 in multistate Markov dependent trials. The probability functions and the probability generating functions of the sooner and later waiting time random variables are studied. Further, the probability generating functions of the distributions of distances between successive occurrences of S0 and between successive occurrences of S0 and S1 and of the waiting time until the rth occurrence of S0 are also given.

scholarly journals Gambling Teams and Waiting Times for Patterns in Two-State Markov Chains

2006 ◽  
Vol 43 (01) ◽  
pp. 127-140 ◽  
Author(s):  
Joseph Glaz ◽  
Martin Kulldorff ◽  
Vladimir Pozdnyakov ◽  
J. Michael Steele
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Generating Function ◽  
Waiting Time ◽  
Waiting Times ◽  
Higher Order ◽  
Expected Value ◽  
Finite Collection

Methods using gambling teams and martingales are developed and applied to find formulae for the expected value and the generating function of the waiting time to observation of an element of a finite collection of patterns in a sequence generated by a two-state Markov chain of first, or higher, order.

Sooner and later waiting time problems for patterns in Markov dependent trials

2003 ◽  
Vol 40 (01) ◽  
pp. 73-86 ◽  
Author(s):  
Qing Han ◽  
Katuomi Hirano
Keyword(s):  
Waiting Time ◽  
Generating Functions ◽  
Random Variables ◽  
Probability Functions ◽  
Probability Generating Functions ◽  
Markov Dependent Trials

In this paper, we investigate sooner and later waiting time problems for patterns S 0 and S 1 in multistate Markov dependent trials. The probability functions and the probability generating functions of the sooner and later waiting time random variables are studied. Further, the probability generating functions of the distributions of distances between successive occurrences of S 0 and between successive occurrences of S 0 and S 1 and of the waiting time until the rth occurrence of S 0 are also given.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Kanwar Sen ◽  
Pooja Mohan ◽  
Manju Lata Agarwal
Keyword(s):  
Waiting Time ◽  
Generating Functions ◽  
Waiting Times ◽  
Waiting Time Distributions ◽  
Probability Generating Functions ◽  
Mean And Variance ◽  
Markov Dependent Trials

We use the Graphical Evaluation and Review Technique (GERT) to obtain probability generating functions of the waiting time distributions of 1st, and th nonoverlapping and overlapping occurrences of the pattern , 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.

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

2012 ◽  
Vol 03 (11) ◽  
pp. 1689-1696
Author(s):  
Bruce J. Chaderjian ◽  
Morteza Ebneshahrashoob ◽  
Tangan Gao
Keyword(s):  
Waiting Time ◽  
Exact Distributions ◽  
Markov Dependent Trials

scholarly journals Gambling Teams and Waiting Times for Patterns in Two-State Markov Chains

2006 ◽  
Vol 43 (1) ◽  
pp. 127-140 ◽  
Author(s):  
Joseph Glaz ◽  
Martin Kulldorff ◽  
Vladimir Pozdnyakov ◽  
J. Michael Steele
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Generating Function ◽  
Waiting Time ◽  
Waiting Times ◽  
Higher Order ◽  
Expected Value ◽  
Finite Collection

Methods using gambling teams and martingales are developed and applied to find formulae for the expected value and the generating function of the waiting time to observation of an element of a finite collection of patterns in a sequence generated by a two-state Markov chain of first, or higher, order.

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