Probability estimation based on grey system theory for simulation evaluation

In the evaluation of some simulation systems, only small samples data are gotten due to the limited conditions. In allusion to the evaluation problem of small sample data, an interval estimation approach with the improved grey confidence degree is proposed. On the basis of the definition of grey distance, three kinds of definition of the grey weight for every sample element in grey estimated value are put forward, and then the improved grey confidence degree is designed. In accordance with the new concept, the grey interval estimation for small sample data is deduced. Furthermore, the bootstrap method is applied for more accurate grey confidence interval. Through resampling of the bootstrap, numerous small samples with the corresponding confidence intervals can be obtained. Then the final confidence interval is calculated from the union of these grey confidence intervals. In the end, the simulation system evaluation using the proposed method is conducted. The simulation results show that the reasonable confidence interval is acquired, which demonstrates the feasibility and effectiveness of the proposed method.