Xiao WangFollow

Date of Completion


Embargo Period



cluster of events, multiple window, moving sum, R

Major Advisor

Joseph Glaz

Associate Advisor

Zhiyi Chi

Associate Advisor

Nitis Mukhopadhyay

Field of Study


Open Access

Open Access


In this dissertation we derive accurate approximations and inequalities for the distribution of fixed window scan statistics for observations from a continuous model. Employing the R algorithms for multivariate normal and t probabilities developed by Genz and Bretz (2009), these approximations and inequalities are applied to normal observations, with mean and variance being both known and unknown. These approximations are utilized to investigate the performance of fixed window scan statistics for detecting a local shift in the process mean for iid normal data. Both one and two dimensional scan statistics are investigated. To detect a local change of unknown size in the process mean, a multiple window scan statistic is introduced and compared with fixed window scan statistics via a power comparison. These results are also extended to ARMA time series data, which consists of dependant observations. It is concluded that both approximations and inequalities are quite accurate, and when the size of a local change in the process mean is unknown, the multiple window scan statistic outperforms fixed window scan statistics.