I have a question. In the maximum likelihood estimator, $\displaystyle \hat{\theta} $ is called maximum likelihood estimator of $\displaystyle \theta $ if value of $\displaystyle \hat{\theta}$ maximizing $\displaystyle f(x_1,x_2,...,x_n|\theta) $. Why we define like this? why not minimum?($\displaystyle f(x_1,x_2,...,x_n|\theta) $ denote probability mass function of the random variable $\displaystyle X_1,..., X_N $.

Can you explain for me?

Thank you very much.