This study proposes a novel approach blending optimum allocation (OA) technique and spectral density estimation to analyse and classify epileptic electroencephalogram (EEG) signals. This study employs the OA to determine representative sample points from the original EEG data and then applies periodogram (PD), autoregressive (AR), and the mixture of PD and AR to extract the discriminative features from each OA sample group. The obtained feature sets are evaluated by three popular machine learning methods: support vector machine (SVM), quadratic discriminant analysis (QDA), and k-nearest neighbour (k-NN). Several output coding approaches of the SVM classifier are tested for selecting the best feature sets. This scheme was implemented on a benchmark epileptic EEG database for evaluation and also compared with existing methods. The experimental results show that the OA_AR feature set yields better performances by the SVM with an overall accuracy of 100%, and outperforms the state-of-the-art works with a 14.1% improvement. Thus, the findings of this study prove that the proposed OA-based AR scheme has significant potential to extract features from EEG signals. The proposed method will assist experts to automatically analyse a large volume of EEG data and benefit epilepsy research.