A suitable method for fitting regression models with the aim of increasing the flexibility of the model in analyzing data types with a non-normal distribution structure is to use the class of normal-scale mixed distributions. The structure of this family is based on a stochastic hierarchical representation in which the mixed distribution plays a fundamental role in the specific statistical properties of these mixed distributions. This representation will lead to a simpler and better application of these distributions in fitting complex models by the Bayesian approach. In this paper, we introduce the normal-scale mixed distribution family and its resulting distributions in fitting panel models in order to perform more robust analyses of dependent data. We also obtain the complete conditional posterior distributions required for parameter estimation using the Gibbs sampling algorithm. In the following, we apply the introduced models in analyzing Tehran Stock Exchange data and compare them with the model selection criteria.