 Open Access

## Abstract

The linear regression model as well as the time series model is applied in many fields, in which the mean of the dependent variable is one function of the mean of the independent variables. However, to consider the regression model following in the Classical Statistics (the Frequent Statistics), it means that the parameters are the constants, in many situations, the regression model does not describe the fluctuation of both the dependent variable and the independent variables. Therefore, we need to modify the parameters following the random variable form, not the constant form, like as the regression in Bayesian Statistics. The other side, when the parameters considered as the random variables, computations in the regression model becomes very complex, because we need to compute the product of the probability distributions. So, we must evaluate about to vary of the variables' probability distributions not only the normal distribution, the Student distribution t, the Poisson distribution, the binomial distribution… In this paper, we estimated the dependent variable's probability distribution form through the simple Bayesian regression model in cases having many the probability distribution forms of the independent variable. In addition, we apply the results to real stock price data, proving that the most appropriate probability distribution with the data is a mixture of probability distributions, not a single normal distribution.

Author's Affiliation
• ### Hoa Thanh Le

Email I'd for correspondance: hoalt@uel.edu.vn

• ### Bao The Pham

Article Details

Issue: Vol 5 No 1 (2021)
Page No.: 1325-1339
Published: Mar 31, 2021
Section: Research article
DOI: Copyright: The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

How to Cite
Le, H., Pham, U., Nguyễn, A., & Pham, B. (2021). The similarity about the probability distributions of variables in the Bayesian regression model and application. VNUHCM Journal of Economics, Business and Law, 5(1), 1325-1339. https://doi.org/https://doi.org/10.32508/stdjelm.v5i1.701