It's my last statistics class for my bachelor's degree, and my midterm is tomorrow, these are some resources I found for these concepts.
Method of Moments and Maximum Likelihood Estimation are two methods for estimating parameters of a distribution.
MoM
Basic Idea: equate sample moments with the respective theoretical moments E(X^k), k=1,2,3.... , until you have as many equations as parameters, and solve for the parameters.
Links
MLE
Basic idea: maximize likelihood of data to estimate unknown parameter 𝛉. Find L(𝛉), log-likelihood it to make it easier to work with, differentiate it, set it to 0, and solve for 𝛉.
Links
- Maximum Likelihood Estimation | STAT 415
- Explaining Maximum Likelihood Estimationf
- MLE.pdf
- Maximum Likelihood by NIST (Pros and Cons)
- Maximum Likelihood, clearly explained by Statquest
- Maximum Likelihood Estimation in Python
MoM vs MLE
MLEs can be shown to be asymptotically efficient, but MLEs require more assumptions. The best tool depends on the situation.