## 2 Materials and Methods
### Feature Parameters  
The mel-frequency cepstral coefficients (MFCCs) and linear prediction cepstrum coefficients (LPCCs) are well known in speech signal processing, and thus, they will not be discussed in detail here [32; 33]. More information about their application and derivation can be found in a number of previous studies [14; 15; 28]. In this work, 20-dimensional MFCCs and 20-dimensional LPCCs were extracted from a 40 ms window signal using a 20 ms frameshift [28].  
Among the various higher-order statistics (HOS), the third- and fourth-order cumulants were used as characteristic parameters in this study. These parameters are called normalized skewness (\(\gamma_{3}\)) and normalized kurtosis (\(\gamma_{4}\)) and they are defined as shown in Equation (1). In this paper, kurtosis is, to be exact, excess kurtosis. Skewness and kurtosis in the time domain have shown massive potential as classification indices for pathological signals [34; 35]. They worked well in the classification between elderly and young voices, as shown in a previous study [5].  
\[\gamma_{3}=\frac{\sum_{n=1}^{N}(x_{n}-\mu)^{3}}{(N-1)\sigma^{3}},\ \gamma_{4}=\frac{\sum_{n=1}^{N}(x_{n}-\mu)^{4}}{(N-1)\sigma^{4}}-3 \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Number of Samples** & **Mean Age** & **Standard Deviation Age** \\ \hline Men (age) & & & \\
22–59 & 24 & 39.13 & 12.76 \\
60–89 & 24 & 72.2 & 7.28 \\ \hline Women (age) & & & \\
20–58 & 39 & 39.12 & 12.57 \\
60–87 & 39 & 70.7 & 8.27 \\ \hline \end{tabular}
\end{table}
Table 1: Descriptive statistics of voice samples used in the study.  
where \(\rm{x_{n}}\) is the \(\rm{n^{th}}\) sample value, N is the number of samples, and \(\rm{\mu}\) and \(\rm{\sigma}\) represent the mean and standard deviation, respectively.  
Skewness indicates the symmetry of the probability density function (PDF) of the amplitude of a time series. A normal distribution has a skewness of zero, which indicates a time series with an equal number of large and small amplitude values. If the skewness value is between \(-0.5\) and \(0.5\), the data are fairly symmetrical. If the skewness value is between \(-1\) and \(-0.5\) or between \(0.5\) and \(1\), the data are moderately skewed. If the skewness value is positive, it indicates a time series with many small values and few large values that is positively skewed (right tail). On the contrary, a time series with many large values and few small values is negatively skewed (left tail), and the skewness values are negative. Kurtosis measures the tailedness of the PDF of a time series. The kurtosis value is often compared with a normal distribution, which is equal to zero in Equation (1). If the kurtosis value is greater than zero, then the time series has relatively sharp peaks and heavier tails than a normal distribution. On the contrary, if the kurtosis is less than zero, then the time series has relatively flat peaks and lighter tails than a normal distribution [28; 36].  
In this study, the parameters of the 20-dimensional MFCCs and the 20-dimensional LFCCs were extracted from a 40 ms window signal using a 20 ms frameshift. The same settings have been applied in many previous studies [28; 37]. Parameters such as MFCC + skewness and LPCC + kurtosis were created by appending one parameter to the original 20-dimensional MFCCs and LPCCs, thus producing 21 dimensions. MFCC + skewness + kurtosis and LPCC + skewness + kurtosis had 22 dimensions. Finally, the MFCC + delta + skewness + kurtosis parameter, which is made up of the 20-dimensional MFCCs, the 20-dimensional MFCC deltas, skewness, and kurtosis, had 42 dimensions. Therefore, the total number of dimensions ranged from 20 to 42. All voice data were grouped into training (70% of the data) and test (30%) sets to implement all methods. For a five-fold cross validation scheme, each set was randomly selected from the subset [35; 38; 39]. The whole process was repeated 10 times and the results were averaged. The results are shown as the mean and standard deviation.