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One of the most widely used statistical topics in research fields is regression problems. In these models, the basic assumption of model errors is their normality, which, in some cases, is different due to asymmetry features or break points in the data. Piecewise regression models have been widely used in various fields, and it is essential to detect the breakpoint. The break points in piecewise regression models are necessary to know when and how the pattern of the data structure changes. One of the major problems is that there is a heavy tail in these data, which has been solved by using some distributions that generalize the normal distribution. In this paper, the piecewise regression model will be investigated based on the scale mixture of the normal distribution. Also, this model will be compared with the standard piecewise regression model derived from normal errors.

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The classification of shape data is a significant challenge in the statistical analysis of shapes and machine learning. In this paper, we introduce a multinomial logistic regression model based on shape descriptors for classifying labeled configurations. In this model, the explanatory variables include a set of geometric descriptors such as area, elongation, convexity, and circularity, while the response variable represents the category of each configuration. The inclusion of these descriptors preserves essential geometric information and enhances classification accuracy. We evaluate the proposed model using both simulated data and real datasets, and the results demonstrate its effective performance. Additionally, the proposed method was compared with one of the existing methods in the literature, and the results indicated its superiority in terms of both classification accuracy and computational simplicity.