Electroencephalogram (EEG) is often used in the confirmatory test for brain death diagnosis in clinical practice. Because EEG recording and monitoring is relatively safe for the patients in deep coma, it is believed to be valuable for either reducing the risk of brain death diagnosis (while comparing other tests such as the apnea) or preventing mistaken diagnosis. The objective of this paper is to study several statistical methods for quantitative EEG analysis in order to help bedside or ambulatory monitoring or diagnosis. We apply signal processing and quantitative statistical analysis for the EEG recordings of 32 adult patients. For EEG signal processing, independent component analysis (ICA) was applied to separate the independent source components, followed by Fourier and time-frequency analysis. For quantitative EEG analysis, we apply several statistical complexity measures to the EEG signals and evaluate the differences between two groups of patients: the subjects in deep coma, and the subjects who were categorized as brain death. We report statistically significant differences of quantitative statistics with real-life EEG recordings in such a clinical study, and we also present interpretation and discussions on the preliminary experimental results.