# Clasification of parameter estimation method

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?

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You only define $\hat P$ but not $P$, hence one cannot answer the question. – Stéphane Laurent Feb 7 '13 at 20:56
Thanks for your reply. I am not quite sure what you mean with $\hat{P}$ and $P$. Is $\hat{P}$ the estimated $P$ and $P$ the real value of $P$? – limp Feb 7 '13 at 21:04
Yes, limp, you need to define the parameter $P$ – Stéphane Laurent Feb 8 '13 at 7:07
Let's say that $P$ is the maximum water pressure coming out from a valve A. Assume that I don’t know anything about valve A, so I have no idea what the water pressure might be. Therefore, in order to estimate $P$, I take a number of water pressure samples from valve A and say that $P$ is estimated to be equal to the maximum water pressure sample acquired. Thanks. – limp Feb 8 '13 at 7:47
Please see my updated question description. – limp Feb 8 '13 at 9:02