Interval estimation of small samples based on grey confidence degree

In many engineering practices, only a small sample data is collected due to the cost restrictions and limiting conditions. In allusion to the evaluation problem of the small sample, interval estimation approach with the improved grey confidence degree is proposed. On the basis of the definition of grey distance, a new definition of the grey weight for every sample element in grey estimated value and a new definition of grey confidence degree are put forward. In accordance with the new concept, more accurate grey interval estimation for small samples is deduced. In addition, according to the new definition, grey interval estimation method for two samples are defined. The grey unilateral confidence interval of small samples based on grey confidence level is also introduced. Finally, several example simulations are conducted. The simulation results show that the reasonable confidence interval is achieved, which demonstrate the feasibility and effectiveness of the proposed method.