|
Activity Number:
|
75
|
|
Type:
|
Contributed
|
|
Date/Time:
|
Sunday, August 6, 2006 : 4:00 PM to 5:50 PM
|
|
Sponsor:
|
Section on Quality and Productivity
|
| Abstract - #306842 |
|
Title:
|
Exact Test for an Epidemic Change in a Sequence of Exponentially Distributed Random Variables
|
|
Author(s):
|
Ping Shing Chan*+ and Kim Fung Lai
|
|
Companies:
|
The Chinese University of Hong Kong and The Chinese University of Hong Kong
|
|
Address:
|
Department of Statistics, Hong Kong, 11111, China
|
|
Keywords:
|
epidemic change ; exact test ; exponential variables ; Wald test
|
|
Abstract:
|
Suppose we have a sequence of independent exponentially distributed observations. We would like to test the hypothesis that the sequence has the same mean versus the alternative hypothesis that there is an epidemic change in the sequence. Epidemic change refers to a change of mean after an unknown point, for an unknown duration in the sequence. We first review the asymptotic null distributions of the Wald test and likelihood ratio test. However these tests are good for large to moderate sample sizes only. In this thesis, we consider the Wald test of the epidemic change when the sample size is small. The null distribution of the statistic is a linear combination of Dirichlet random variables. A recursive formula has been derived to obtain the probabilities. The critical values are then tabulated. The powers of this exact test and its asymptotic counterpart are then compared.
|
