Maximum likelihood estimation for single server queues from waiting time data

1996 ◽  
Vol 24 (1-4) ◽  
pp. 155-167 ◽  
Author(s):  
Ishwar V. Basawa ◽  
U. Narayan Bhat ◽  
Robert Lund
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Waiting Time ◽  
Likelihood Estimation ◽  
Single Server ◽  
Time Data ◽  
Single Server Queues

Maximum likelihood estimation for stochastic rth-order reactions. II

1973 ◽  
Vol 10 (02) ◽  
pp. 441-446
Author(s):  
John P. Mullooly
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Waiting Time ◽  
Likelihood Estimation ◽  
Initial Number ◽  
Asymptotically Normal ◽  
Reaction Event ◽  
Wide Range ◽  
Order Case ◽  
Exact Maximum Likelihood

In this paper we consider maximum likelihood estimation of the rate constant for stochastic rth-order reactions based on observation of the level of the system at time t > 0. Conditions are found for which the waiting time until the nth. reaction event is asymptotically normal, as the initial number of molecules and the number of reaction events become large. This distributional result is used to derive an approximate estimator which is shown for the second-order case to be close to the exact maximum likelihood estimate over a wide range of percentage completion.

Maximum likelihood estimation for stochastic rth-order reactions. II

1973 ◽  
Vol 10 (2) ◽  
pp. 441-446 ◽  
Author(s):  
John P. Mullooly
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Waiting Time ◽  
Likelihood Estimation ◽  
Initial Number ◽  
Asymptotically Normal ◽  
Reaction Event ◽  
Wide Range ◽  
Order Case ◽  
Exact Maximum Likelihood

In this paper we consider maximum likelihood estimation of the rate constant for stochastic rth-order reactions based on observation of the level of the system at time t > 0. Conditions are found for which the waiting time until the nth. reaction event is asymptotically normal, as the initial number of molecules and the number of reaction events become large. This distributional result is used to derive an approximate estimator which is shown for the second-order case to be close to the exact maximum likelihood estimate over a wide range of percentage completion.

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