Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
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
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.

share|cite|improve this answer
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
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
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.