The current era demands high quality software in a limited time period to achieve new goals and heights. To meet user requirements, the source codes undergo frequent modifications which can generate the bad smells in software that deteriorate the quality and reliability of software. Source code of the open source software is easily accessible by any developer, thus frequently modifiable. In this paper, we have proposed a mathematical model to predict the bad smells using the concept of entropy as defined by the Information Theory. Open-source software Apache Abdera is taken into consideration for calculating the bad smells. Bad smells are collected using a detection tool from sub components of the Apache Abdera project, and different measures of entropy (Shannon, Rényi and Tsallis entropy). By applying non-linear regression techniques, the bad smells that can arise in the future versions of software are predicted based on the observed bad smells and entropy measures. The proposed model has been validated using goodness of fit parameters (prediction error, bias, variation, and Root Mean Squared Prediction Error (RMSPE)). The values of model performance statistics ( $R^2$ , adjusted $R^2$ , Mean Square Error (MSE) and standard error) also justify the proposed model. We have compared the results of the prediction model with the observed results on real data. The results of the model might be helpful for software development industries and future researchers.

Presence of code smells complicate the source code and can obstruct the development and functionality of the software project. As they represent improper behavior that might have an adverse effect on software maintenance, code smells are behavioral in nature. Python is widely used for various software engineering activities and tends tool to contain code smells that affect its quality. This study investigates five code smells diffused in 20 Python software comprising 10550 classes and analyses its severity index using metric distribution at the class level. Subsequently, a behavioral analysis has been conducted over the considered modification period (phases) for the code smell undergoing class change proneness. Furthermore, it helps to investigate the accurate multinomial classifier for mining the severity index. It witnesses the change in severity at the class level over the modification period by mapping its characteristics over various statistical functions and hypotheses. Our findings reveal that the Cognitive Complexity of code smell is the most severe one. The remaining four smells are centered around the moderate range, having an average severity index value. The results suggest that the J48 algorithm was the accurate multinomial classifier for classifying the severity of code smells with 92.98% accuracy in combination with the AdaBoost method. The findings of our empirical evaluation can be beneficial for the software developers to prioritize the code smells in the pre-refactoring phase and can help manage the code smells in forthcoming releases, subsequently saving ample time and resources spent in the development and maintenance of software projects.