Piecewise Regression Model Based on Scale Mixture Normal Distribution

mentation and obtaining trusted optimal answers can be the main reason for this method.We will use the EM algorithm to estimate the model parameters, i.e., the vector.To implement this algorithm, it is assumed that there are also hidden observations for the observed data. Results and DiscussionAccording to the observations in the tables, the average values of TPR and FPR in the CN-BP model are respectively higher and lower than in the t-BP model.Also, the value of TPR decreases in both models as the sample size increases.With the increase in the sample size, the value of FPR increases in both models.Therefore, the CN-BP model is better than the t-BP model in detecting outliers. ConclusionIn this article, we proposed a method to solve piecewise regression problems with errors from scale mixture normal (SMN) distribution by using finite mixed models.Finding change points is similar to categorizing similar observations into groups in mixed models.We created regression lines to estimate change points.Also, using the shown simulations, outlier locations are identified using some special modes of the SMN model.In addition, this numerical study, with actual and simulated data sets, shows the performance of the superior model proposed.As a result, the proposed SMN breakpoint (SMN-BP) model usually gives accurate estimates of change points and regression lines.Therefore, the SMN-BP model is suitable for solving piecewise regression problems.Piecemeal regression can be applied to problems with an important change point, such as quality control, medicine, economics, and decision-making decision-making.