Abstract: In order to solve the problem that the maximum likelihood estimation method (Mle) may produce large errors in solving the distributed parameters in the case of small data samples, the B-MLE method is proposed based on Bootstrap data expansion. Firstly, the Bootstrap method was used to resample the small sample data to generate multiple groups of regenerated samples, so as to expand the data sample. Secondly, the maximum likelihood estimation is used to solve the distribution parameters of the regenerated samples, and the maximum likelihood estimation of multiple parameters is obtained. The probability density function is obtained directly from the parameter estimation by using the kernel density estimation method. Finally, at a given confidence level, the confidence interval of parameters is determined to obtain the confidence interval of reliability. The feasibility and credibility of the proposed method are verified by Monte Carlo method. The results show that the proposed method can reduce the error of maximum likelihood estimation.

Key words: maximum likelihood estimation, bootstrap method, kernel density estimation, probability density function, Monte Carlo simulation