Consider that $P$ is the water pressure coming out from a valve A, therefore, the population is all the valve A pressure values. Let $P_{dif}$ be defined as the difference between the maximum and the minimum pressure of valve A, i.e. $P_{dif}:= P_{max} - P_{min}$.
Now, what I want to do is to estimate $P_{dif}$. In order to do that, I take a number of water pressure samples from valve A. Let $S$ be a set of 3 measured samples ($S = \{X_1 = 5, X_2 = 7, X_3 = 1\}$), i.e. $S$ contains 3 random sample drawn from the population. Therefore, I then say that $ \hat{P_{dif}} = 7 – 1 = 6$.
I am a bit confused as to how to classify this parameter estimation method that I used. How is this parameter estimation method called? Is it a maximum likelihood estimation and if not, what is it?
Thanks in advance.
What you are computing is called the sample range. It is called and L-estimator. You could look at the discussion here.