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

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.

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.

On ordered series and later waiting time distributions in a sequence of Markov dependent multistate trials

2003 ◽  
Vol 40 (3) ◽  
pp. 623-642 ◽  
Author(s):  
James C. Fu ◽  
Yung-Ming Chang
Keyword(s):  
Markov Chain ◽  
Waiting Time ◽  
Generating Functions ◽  
Finite Markov Chain ◽  
Finite Markov Chain Imbedding ◽  
Waiting Time Distributions ◽  
Markov Chain Imbedding ◽  
Exact Distributions ◽  
Markov Chain Imbedding Technique ◽  
Comprehensive Study

The sooner and later waiting time problems have been extensively studied and applied in various areas of statistics and applied probability. In this paper, we give a comprehensive study of ordered series and later waiting time distributions of a number of simple patterns with respect to nonoverlapping and overlapping counting schemes in a sequence of Markov dependent multistate trials. Exact distributions and probability generating functions are derived by using the finite Markov chain imbedding technique. Examples are given to illustrate our results.

On exact and large deviation approximation for the distribution of the longest run in a sequence of two-state Markov dependent trials

2003 ◽  
Vol 40 (02) ◽  
pp. 346-360 ◽  
Author(s):  
James C. Fu ◽  
Liqun Wang ◽  
W. Y. Wendy Lou
Keyword(s):  
Large Deviation ◽  
Finite Markov Chain ◽  
Finite Markov Chain Imbedding ◽  
Markov Chain Imbedding ◽  
Longest Run ◽  
Exact Distributions ◽  
Markov Dependent Trials ◽  
Success Run ◽  
Longest Success Run ◽  
Theoretical Results

Consider a sequence of outcomes from Markov dependent two-state (success-failure) trials. In this paper, the exact distributions are derived for three longest-run statistics: the longest failure run, longest success run, and the maximum of the two. The method of finite Markov chain imbedding is used to obtain these exact distributions, and their bounds and large deviation approximation are also studied. Numerical comparisons among the exact distributions, bounds, and approximations are provided to illustrate the theoretical results. With some modifications, we show that the results can be easily extended to Markov dependent multistate trials.

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.

On ordered series and later waiting time distributions in a sequence of Markov dependent multistate trials

2003 ◽  
Vol 40 (03) ◽  
pp. 623-642 ◽  
Author(s):  
James C. Fu ◽  
Yung-Ming Chang
Keyword(s):  
Markov Chain ◽  
Waiting Time ◽  
Generating Functions ◽  
Finite Markov Chain ◽  
Finite Markov Chain Imbedding ◽  
Waiting Time Distributions ◽  
Markov Chain Imbedding ◽  
Exact Distributions ◽  
Markov Chain Imbedding Technique ◽  
Comprehensive Study

The sooner and later waiting time problems have been extensively studied and applied in various areas of statistics and applied probability. In this paper, we give a comprehensive study of ordered series and later waiting time distributions of a number of simple patterns with respect to nonoverlapping and overlapping counting schemes in a sequence of Markov dependent multistate trials. Exact distributions and probability generating functions are derived by using the finite Markov chain imbedding technique. Examples are given to illustrate our results.

On exact and large deviation approximation for the distribution of the longest run in a sequence of two-state Markov dependent trials

2003 ◽  
Vol 40 (2) ◽  
pp. 346-360 ◽  
Author(s):  
James C. Fu ◽  
Liqun Wang ◽  
W. Y. Wendy Lou
Keyword(s):  
Large Deviation ◽  
Finite Markov Chain ◽  
Finite Markov Chain Imbedding ◽  
Markov Chain Imbedding ◽  
Longest Run ◽  
Exact Distributions ◽  
Markov Dependent Trials ◽  
Success Run ◽  
Longest Success Run ◽  
Theoretical Results

Consider a sequence of outcomes from Markov dependent two-state (success-failure) trials. In this paper, the exact distributions are derived for three longest-run statistics: the longest failure run, longest success run, and the maximum of the two. The method of finite Markov chain imbedding is used to obtain these exact distributions, and their bounds and large deviation approximation are also studied. Numerical comparisons among the exact distributions, bounds, and approximations are provided to illustrate the theoretical results. With some modifications, we show that the results can be easily extended to Markov dependent multistate trials.

Predictors of waiting time for liver TX: A three-year experience

2001 ◽  
Vol 120 (5) ◽  
pp. A370-A370
Author(s):  
C BOBROWSKI ◽  
H GHADIMPOOR ◽  
M STENECK ◽  
X ROGIERS ◽  
C BROELSCH ◽  
...  
Keyword(s):  
Waiting Time
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