Johnson\u27s system of distributions and microarray data analysis

Microarray technology permit us to study the expression levels of thousands of genes simultaneously. The technique has a wide range of applications including identification of genes that change their expression in cells due to disease or drug stimuli. The dissertation is addressing statistical methods for the selection of differentially expressed genes in two experimental conditions. We propose two different methods for the selection of differentially expressed genes. The first method is a classical approach, where we consider a common distribution for the summary measure of equally expressed genes. To estimate this common distribution, the Johnson system of distribution is used. The advantage of using Johnson system is that, there is no need of a parametric assumption for gene expression data. In contrast to other classical methods, in the proposed method, there is a sharing of information across the genes by the assumption of a common distribution for the summary measure of equally expressed genes. The second method is the gene selection using a mixture model approach and Baye\u27s theorem. This approach also uses the Johnson System of distribution for the estimation of distribution of summary measure. Johnson system of distribution has the flexibility of covering a wide variety of distributional shapes. This system provides a unique distribution corresponding to each pair of mathematically possible values of skewness and kurtosis. The significant flexibility of Johnson system is very useful in characterizing the complicated data set like microarray data. In this dissertation we propose a novel algorithm for the estimation of the four parameters of the Johnson system