Sampling from Applied Probability Models

Author(s):  
Eric A. Suess ◽  
Bruce E. Trumbo
1994 ◽  
Vol 26 (3) ◽  
pp. 728-755 ◽  
Author(s):  
Ioannis I. Gerontidis

We consider an absorbing semi-Markov chain for which each time absorption occurs there is a resetting of the chain according to some initial (replacement) distribution. The new process is a semi-Markov replacement chain and we study its properties in terms of those of the imbedded Markov replacement chain. A time-dependent version of the model is also defined and analysed asymptotically for two types of environmental behaviour, i.e. either convergent or cyclic. The results contribute to the control theory of semi-Markov chains and extend in a natural manner a wide variety of applied probability models. An application to the modelling of populations with semi-Markovian replacements is also presented.


1994 ◽  
Vol 26 (03) ◽  
pp. 728-755 ◽  
Author(s):  
Ioannis I. Gerontidis

We consider an absorbing semi-Markov chain for which each time absorption occurs there is a resetting of the chain according to some initial (replacement) distribution. The new process is a semi-Markov replacement chain and we study its properties in terms of those of the imbedded Markov replacement chain. A time-dependent version of the model is also defined and analysed asymptotically for two types of environmental behaviour, i.e. either convergent or cyclic. The results contribute to the control theory of semi-Markov chains and extend in a natural manner a wide variety of applied probability models. An application to the modelling of populations with semi-Markovian replacements is also presented.


1988 ◽  
Vol 25 (A) ◽  
pp. 31-43 ◽  
Author(s):  
Marcel F. Neuts

This is a discussion of the place of empirical methods in the study of probability models. It is argued that, for models of great complexity, careful experimentation may be a legitimate source of factual information on the behavior of such models. The need for rigorous standards of empirical methodology and of appropriate reporting is stressed. A simple, but interesting question on the distribution of the maximal eigenvalue of positive matrices with random elements is used as an example of an experimental study. In the course of the discussion of that example, several operational rules of sound computer experimentation are stated.


1988 ◽  
Vol 25 (A) ◽  
pp. 31-43
Author(s):  
Marcel F. Neuts

This is a discussion of the place of empirical methods in the study of probability models. It is argued that, for models of great complexity, careful experimentation may be a legitimate source of factual information on the behavior of such models. The need for rigorous standards of empirical methodology and of appropriate reporting is stressed. A simple, but interesting question on the distribution of the maximal eigenvalue of positive matrices with random elements is used as an example of an experimental study. In the course of the discussion of that example, several operational rules of sound computer experimentation are stated.


2002 ◽  
Vol 56 (3) ◽  
pp. 248-248
Author(s):  
Stergios B Fotopoulos

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