GERT analysis of m-consecutive-k-out-of-n:F system with overlapping runs and (k 1)-step Markov dependence

2008 ◽  
Vol 3 (1/2) ◽  
pp. 36 ◽  
Author(s):  
Manju Agarwal ◽  
Pooja Mohan
Keyword(s):  
Markov Dependence

More on n-point, win-by-k games

1996 ◽  
Vol 33 (2) ◽  
pp. 382-387 ◽  
Author(s):  
John Haigh
Keyword(s):  
Bernoulli Trials ◽  
Probabilistic Argument ◽  
Domain Of Applicability ◽  
Markov Dependence

When Siegrist (1989) derived an expression for the probability that player A wins a game that consists of a sequence of Bernoulli trials, the winner being the first player to win n trials and have a lead of at least k, he noted the desirability of giving a direct probabilistic argument. Here we present such an argument, and extend the domain of applicability of the results beyond Bernoulli trials, including cases (such as the tie-break in lawn tennis) where the probability of winning each trial cannot reasonably be taken as constant, and to where there is Markov dependence between successive trials.

scholarly journals On Determining the Order of Markov Dependence of an Observed Process Governed by a Hidden Markov Model

2002 ◽  
Vol 10 (3) ◽  
pp. 241-251 ◽  
Author(s):  
R.J. Boys ◽  
D.A. Henderson
Keyword(s):  
Markov Chain ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Real Data ◽  
Information Criteria ◽  
Monte Carlo Algorithm ◽  
Model Parameters ◽  
Markov Dependence ◽  
Finite State

This paper describes a Bayesian approach to determining the order of a finite state Markov chain whose transition probabilities are themselves governed by a homogeneous finite state Markov chain. It extends previous work on homogeneous Markov chains to more general and applicable hidden Markov models. The method we describe uses a Markov chain Monte Carlo algorithm to obtain samples from the (posterior) distribution for both the order of Markov dependence in the observed sequence and the other governing model parameters. These samples allow coherent inferences to be made straightforwardly in contrast to those which use information criteria. The methods are illustrated by their application to both simulated and real data sets.

Robust MIPA array processors with bivariate and Markov dependence

1995 ◽  
Vol 85 (1-3) ◽  
pp. 63-86 ◽  
Author(s):  
Mohammed Ketel ◽  
Ludwik Kurz
Keyword(s):  
Markov Dependence ◽  
Array Processors
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