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Maximum Likelihood theory is widely applied in the scientific research. Generally, it can send the message that the relevant parameters of the population distribution can be estimated by the corresponding samples and provide the ideology to obtain the value of the estimators. This paper aims at demonstrating the development of the ML theory in order to have a relatively clear cognition about the theory. The paper generalizes the principle of the statistics theory and reviews several theoretical and empirical improvement and application based on the ML theory, including distribution parameter estimation in statistics, uncertainty regression in econometrics, and the assimilation of the precipitation radar observation, forming an outline about the current advance of the theory and algorithms and having some outlooks about the future development orientations in potential. In addition, some instructions are presented to approach ML theory and do further research as the basis. These results shed light on guiding further exploration of ML theory. |
