Methodology for Statistical Distribution Determination of Various Data Sources

For uncertainty involved design optimization problems, it requires that the distributions of all concerned design variables and parameters are known. Aiming to determining the statistical distributions of data for all possible cases, corresponding methods are investigated in this study. For random variables where samples are abundant, some kind of apriori distributions are fitted to available data, and the best fitted distribution is selected as the final choice for further sampling. As for small sample data, provided data are not sufficient to determine which distribution can fit them well for the result obtained in this way has much uncertainty. A Bayesian inference method is adopted to account for this issue. Noting that the Bootstrap algorithm has its advantages in determining statistical distribution parameters for scarce random data, it is also studied here for comparison. Results of this research show that the overall methodology can find an appropriate distribution for various data sources.