|
Activity Number:
|
77
|
|
Type:
|
Contributed
|
|
Date/Time:
|
Monday, August 12, 2002 : 8:30 AM to 10:20 AM
|
|
Sponsor:
|
Section on Physical & Engineering Sciences*
|
| Abstract - #301486 |
|
Title:
|
Estimation For Thinned Poisson Processes With Discretized Rates
|
|
Author(s):
|
Greg Miller*+
|
|
Affiliation(s):
|
Stephen F. Austin State University
|
|
Address:
|
1936 North Street, Box 13040, Nacogdoches, Texas, 75962-3040, USA
|
|
Keywords:
|
Integer maximum likelihood ; discrete parameter space ; exponential distribution ; Erlang distribution ; consistency ; M/M/s queue
|
|
Abstract:
|
Estimation for a class of thinned Poisson processes is our motivating problem. Analyzing this class leads to the derivation of the maximum likelihood estimator (MLE) for the integer-restricted parameter of an exponential distribution. Due to the discrete nature of the parameter space, the probability of estimating the parameter without error is used as the criterion of efficiency. The integer MLE is proven to be consistent in the discrete sense, meaning that the probability of correct estimation approaches one as the sample size increases. The discrete sampling distribution of the estimator is obtained, and a comparison with a natural competing estimator shows that the integer MLE is preferable for smaller sample sizes. Several areas of application are discussed, including Poisson processes embedded in Markovian queues. These examples illustrate the type of problems for which the results are useful.
|
