Parameter estimation of mixed two distributions based on EM algorithm and Nelder-Mead algorithm

Abstract

As the amount of data increases, the data can obey either a single distribution, two distributions or even multiple distributions. If the distribution parameters and mixing ratio can be estimated for mixed data, it will be beneficial to further analysis and research in practical applications. In this paper, the EM algorithm and the Nelder-Mead(NM) algorithm are applied to the mixed parameter estimation of the two distributions, including mixing two identical distributions, mixing two different distributions, and comparing the EM algorithm and the Nelder-Mead algorithm to estimate the accuracy of the mixed distribution parameter estimation and its initial comparison. The stability of the value and other advantages and disadvantages. A large amount of data simulation results found that the EM algorithm has a good effect on the estimation of mixed distribution parameters, with high accuracy and fast convergence. The initial value selection has little effect on the results, and the preliminary derivation process is more complicated; the Nelder-Mead algorithm has a good effect on the estimation of mixed distribution parameters. High precision, fast convergence speed, the initial value selection has a greater impact on the result, the preliminary derivation process is relatively simple, and the application range is wide. When the initial value is close to the peak value of the real data, the parameter estimation effect is better; the two algorithms have poorer effect on the unimodal distribution parameter estimation for the data, and the bimodal distribution parameter estimation effect is better.