Prediction method of the transformed data

In Meteorology, we often get data products we need by doing statistical analysis to observation data. It´s very important for meteorology forecasting and disaster warning. When we do statistic modeling, the data are not always normal distribution, so we transform the data to a new one first and then modeling. In this paper, we mainly consider how to forecast origin variable from experience model forecast value. On this question, people always consider less about the error from inverse transformation. We mainly use Monte Carlo method, which can be used to deal with kinds of transform function. In the third part, I have simulated logarithmic transformation to compare RMSE of Monte Carlo method and inverse. It can be see that Monte Carlo can decrease origin variable´s prediction error.