Tracheoesophageal (TE) speech is generated by patients who have undergone a total laryngectomy where the larynx (voice box) is removed and replaced by a tracheoesophageal puncture. This work presents a novel low complexity algorithm to estimate the degree of severity of disordered TE speech. The proposed algorithm has two output scores which are computed from 20 ms voiced frames of the speech signal. An 18th order Linear Prediction (LP) analysis is performed on each voiced frame of the speech signal. The first output score uses features derived from high order statistics (mean, variance, skewness and kurtosis) which are calculated from the LP coefficients, the cepstral coefficients and the LP residual signal. These high order statistics (HOS) along with the pitch value are averaged over all voiced frames yielding a total of 14 HOS quality features. The second output score is derived from features derived from the estimated vocal tract model parameters (cross-sectional tubes areas). Statistical vocal tract parameters (VTPs) across all voiced speech frames were used as speech quality features. Forward stepwise regression as well as K-fold cross validation are then used to select the best sets of features to be fed to the regression models. The results show high correlations with subjective scores for several regression techniques that can provide a correlation up to 0.91 when VTP-Gaussian model is used.