Date of Completion

8-8-2019

Embargo Period

8-7-2019

Keywords

scan statistics, local change, gamma distribution, exponential distribution, scale parameter

Major Advisor

Joseph Glaz

Associate Advisor

Nitis Mukhopadhyay

Associate Advisor

Richard A. Vitale

Field of Study

Statistics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

In this dissertation scan statistics for detecting a local change in the scale parameter for gamma and exponential random variables are investigated for both one dimensional and two dimensional cases. The shape parameter is assumed to be known for the gamma random variables. When the size of the window where the local change occurs is known but the scale parameter in null hypothesis is unknown, conditional fixed window scan statistics are proposed. When the true window size is unknown, conditional multiple window minimum $p$-value scan statistics and variable window scan statistics based on generalized likelihood ratio test principle are developed. The performance of the proposed scan statistics is evaluated by Monte Carlo simulation studies. For moderate to large shift in scale parameter, conditional fixed window scan statistics with the correct scanning window size, multiple window and variable window scan statistics all performed well.

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