Tukey GH is a transformed normal distribution, having two parameters (g,h). The g parameter represents skew measuring, and the h represents kurtosis measuring. Our motivation is to affect these parameters on the behavior for a simulation data and real data, such as the Iraqi stock market Index (ISX60) and the Standard and Poor's (SP500) index using the Bayesian framework. Then, our aim is to find the estimation for the parameters in this distribution using empirical and parametric Bayesian methods, and study the effective on the simulation and real data. The simulation study will be shown the behavior of the parameters with a different number of sampling and prior distributions. We will use the real data from ISX60 and SP500 index.