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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.

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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

1 Answer 1

up vote 0 down vote accepted

What you are computing is called the sample range. It is called and L-estimator. You could look at the discussion here.

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Thanks very much. That gives me a clue as to where to search. So, I guess that this is not a point estimation, right? –  limp Feb 8 '13 at 10:37
1  
It is a point estimator. –  Learner Feb 8 '13 at 10:51
    
So, it is a point estimator using an L-estimator method? –  limp Feb 8 '13 at 11:01
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The categories of point estimators and L-estimators are not mutually exclusive. An estimator is not a method, it is a random variable (computed from the sample which is random) that hopefully has good properties when it comes to shedding light about the quantities you would like to learn about. –  Learner Feb 8 '13 at 11:06
    
I recommend studying the concept of an estimator in a good mathematical statistics textbook (such as Casella and Berger's). –  Learner Feb 8 '13 at 11:08

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