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Yu, XiaominSimulation Study of Sequential Probability Ratio Test (SPRT) in Monitoring an Event Rate
MS, University of Cincinnati, 2009, Medicine : Biostatistics (Environmental Health)
Unlike the classical hypothesis test, the method of sequential probability ratio test (SPRT) checks the outcome sequentially. Based on the outcome, the test can have one of three test results: reject the null hypothesis, accept the null hypothesis, or continue the SPRT procedure. Consequently, the SPRT method may reduce the required sample size for performing a test as compared to a classical hypothesis test. A simulation study of SPRT was performed. A variety of comparisons between p0 and p1 were simulated with p0 =0.001 and p1 between 0.0011 and 0.0023. The target rates of the 12 time points for each group were from 0 out of 104 to 30 out of 104 with a constant increment of 2/104. The results showed that the larger the difference between p0 and p1, the quicker one could reject the null hypothesis. Therefore, we can expect a quicker response when p0/p1 has larger differences.

Committee:

Paul Succop (Committee Chair); Linda Levin (Committee Member)

Subjects:

Biostatistics; Epidemiology; Health Care; Mathematics; Statistics; Therapy

Keywords:

SPRT; Sequential Probability Ratio Test; Sequential Test; Simulation Study.

Al-Mafrachi, Basheer Husham AliDetection of DDoS Attacks against the SDN Controller using Statistical Approaches
Master of Science in Computer Engineering (MSCE), Wright State University, 2017, Computer Engineering
In traditional networks, switches and routers are very expensive, complex, and inflexible because forwarding and handling of packets are in the same device. However, Software Defined Networking (SDN) makes networks design more flexible, cheaper, and programmable because it separates the control plane from the data plane. SDN gives administrators of networks more flexibility to handle the whole network by using one device which is the controller. Unfortunately, SDN faces a lot of security problems that may severely affect the network operations if not properly addressed. Threat vectors may target main components of SDN such as the control plane, the data plane, and/or the application. Threats may also target the communication among these components. Among the threats that can cause significant damages include attacks on the control plane and communication between the controller and other networks components by exploiting the vulnerabilities in the controller or communication protocols. Controllers of SDN and their communications may be subjected to different types of attacks. DDoS attacks on the SDN controller can bring the network down. In this thesis, we have studied various form of DDoS attacks against the controller of SDN. We conducted a comparative study of a set of methods for detecting DDoS attacks on the SDN controller and identifying compromised switch interfaces. These methods are sequential probability ratio test (SPRT), count-based detection (CD), percentage-based detection (PD), and entropy-based detection (ED). We implemented the detection methods and evaluated the performance of the methods using publicly available DARPA datasets. Finally, we found that SPRT is the only one that has the highest accuracy and F score and detect almost all DDoS attacks without producing false positive and false negative.

Committee:

Bin Wang, Ph.D. (Advisor); Yong Pei, Ph.D. (Committee Member); Mateen Rizki, Ph.D. (Committee Member)

Subjects:

Computer Engineering

Keywords:

SDN; Controller; DDoS attacks; SPRT; CD; PD; CUSUM; ED

Starvaggi, Patrick WilliamExact Distributions of Sequential Probability Ratio Tests
PHD, Kent State University, 2014, College of Arts and Sciences / Department of Mathematical Science
We have found the joint Laplace transform of certain stopping times related to the SPRT and their associated stopped processes for testing the mean of an exponential population. This gives the exact distribution of the stopping time associated with this SPRT. The method used is novel and bypasses the usual martingale techniques. From this have derived the variance of this SPRT, a result which was hitherto unknown. We also have made a novel comparison of a fixed sample Neyman-Pearson most powerful test to Wald's SPRT, whose sample size is random. This was done by analogy to mean-variance analysis in portfolio theory. The random sample number of the SPRT brings that "risk" with it, and therefore, that variability should be brought into the discussion when comparing the guaranteed fixed sample size of the Neyman-Pearson test. The technique used is flexible and can be extended to study stopping times of the same probability ratios using non-constant boundaries, known as generalized SPRT (GSPRT). We considered the case when the boundaries are intersecting lines. This means that the GSPRT will be bounded by some fixed N>0 with probability one. We have provided a closed form expression for the joint Laplace transform of this GSPRT and the associated stopped process. We thereby provided closed form expressions for the first two moments of the GSPRT.

Committee:

Mohammad Khan (Advisor); Eugene Gartland, Jr. (Committee Member); Oana Mocioalca (Committee Member); Butje Patuwo (Committee Member); Manfred Van Dulmen (Committee Member)

Subjects:

Mathematics

Keywords:

Sequential probability ratio test, SPRT, GSPRT, exponential distribution, Neyman-Pearson