method of moments of an uniform distribution

Question

Let $ X_1, ... X_n $ a sample of independent random variables with uniform distribution $(0,$$ \theta $$ ) $ Find a $ $$ \widehat\theta $$ $ estimator for theta using the method of moments Thanks

I think using the indicatrix used in this type of problems that can not be derived, but not as used

score 6 · Answer 1 · answered Jul 04 '11 at 18:13

6

To find the method of moments, you equate the first $k$ sample moments to the corresponding $k$ population moments. You then solve the resulting system of equations simultaneously.
Here note that the first sample moment when $k=1$ is the sample mean. That is $\displaystyle\frac{1}{n} \sum_{i=1}^{n}X_i^1=\bar{X}$. The first population moment is just the expectation of Uniform$(0,\theta)$, which is given by $\mathrm{E}(X_i)=\theta/2$.
So the method of moments estimator is the solution to the equation $$\frac{\hat{\theta}}{2}=\bar{X}.$$

answered Jul 04 '11 at 18:13

Nana

8,717

sorry i wanted the estimator of maximun verisimilitude )= – Daniel Jul 05 '11 at 03:34
Do you mean the MLE? – Nana Jul 05 '11 at 03:51
yes, i mean the MLE :D – Daniel Jul 05 '11 at 04:17
oh ok. could you post it as a different question then (Since the above question deals with the method of methods). I'll do my best to help...:) – Nana Jul 05 '11 at 04:22

score 3 · Answer 2 · answered Jul 04 '11 at 18:05

3

Just set the empirical average $\bar X$ equal to $E[X_1] = \frac \theta 2$. This gives $\hat \theta = 2 \bar X$, correct?

answered Jul 04 '11 at 18:05

guy

4,620

method of moments of an uniform distribution

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