This work is focused on deep learning methods, such as feedforward neural network (FNN) and convolutional neural network (CNN), for pathological voice detection using mel-frequency cepstral coefficients (MFCCs), linear prediction cepstrum coefficients (LPCCs), and higher-order statistics (HOSs) parameters. In total, 518 voice data samples were obtained from the publicly available Saarbruecken voice database (SVD), comprising recordings of 259 healthy and 259 pathological women and men, respectively, and using /a/, /i/, and /u/ vowels at normal pitch. Significant differences were observed between the normal and the pathological voice signals for normalized skewness (p = 0.000) and kurtosis (p = 0.000), except for normalized kurtosis (p = 0.051) that was estimated in the /u/ samples in women. These parameters are useful and meaningful for classifying pathological voice signals. The highest accuracy, 82.69%, was achieved by the CNN classifier with the LPCCs parameter in the /u/ vowel in men. The second-best performance, 80.77%, was obtained with a combination of the FNN classifier, MFCCs, and HOSs for the /i/ vowel samples in women. There was merit in combining the acoustic measures with HOS parameters for better characterization in terms of accuracy. The combination of various parameters and deep learning methods was also useful for distinguishing normal from pathological voices.