AbstractsMathematics

In many practical applications, it has been observed that there might exist changes in real data sets. By noticing those changes, people can make the best decisions to achieve benefits and avoid losses. The problem of change point analysis always means identifying the number and the locations of change points. Schwarz (1978) introduced a new model selection criterion named Schwarz Information Criterion (SIC), which is mathematically tractable and widely used in change point detection problems. In this thesis, statistical analysis of Weibull distribution related to application of Schwarz Information Criterion (SIC), modified Schwarz Information Criterion (MIC), and improved Schwarz Information Criterion (IIC) will be explored. Among these information criteria, MIC was published by Chen et al. (2006); and IIC is a conjecture suggested in this thesis.In the first parts of Chapter 2, 3, and 4, corresponding to SIC, MIC, and IIC, the theoretical basis and mathematical formula have been derived. The Weibull distribution is employed in each situation to be the specific models. After theoretical derivation, in the second parts, simulation tests for each proposed situations are conducted to estimate the performance of the information criteria. Power comparisons with the suggested simulation tests are investigated to compare the performance of all three information criteria. The change point location has been changed to indicate the variety of performance of detecting procedures. In the last part of each chapter, applications to real data sets are provided to illustrate the testing procedures based on each information criterion.The only difference among these three information criteria are their penalty terms. The idea of this thesis is to compare the performance of each model selection information criterion and to figure out the rule of improving the power of change point detection procedure. Advisors/Committee Members: Ning, Wei (Advisor).