MSNBurr and MSTBurr distribution have been developed as Neo-Normal distributions that represent a relaxation of normality. The difference between them is that the MSTBurr's peak is below MSNBurr's. In this paper, we propose a MSEPBurr distribution with its peak could be not only lower but also high-er than MSNBurr. Furthermore, we study several properties of MSEPBurr, such as mean, variance, skewness, kurtosis, and quantile. The MSEPBurr parameters are estimated by using the Bayesian approach with the BUGS language implementation for its computation. We employ simulation study and use existing data to illustrate the application of the regression model. In real data, we notice that MSEPBurr has similar performance with MSNBurr and MSTBurr that they outperform Normal and Student-t distribution in Australian athlete data because their skewness can accommodate long left tail excellently. However, their performance is less than the Student-t model in chemical reaction rate data because their skewness can not accommodate long right tail perfectly. Although in general their perfor-mance is the same, we observe that the MSEPBurr performs better than the MSNBurr and the MSTBurr in some simulated data.