Parameter Estimation: Statistics

lindah · 2011-06-01 13:44:48

http://img202.imageshack.us/i/64221633.png/

I have a feeling what I have done is wrong since one parameter shouldn't be expressed in another?

Thanks in advance for any feedback
Lin

Last edited by lindah (2011-06-24 13:35:10)

bobbym · 2011-06-01 17:23:49

Hi lindah;

Welcome to the forum.

How did you get the first and second moments?

lindah · 2011-06-01 17:51:08

Hi bobby,

I first looked for E[X] by calculating:

Then I equated that to or and solved for a.

For E[X^2] I did the same:

I am not completely sure how to go about method of moments, since for most examples - at this step onwards it jumps to the answer very rapidly and I can't follow

EDIT: Typo

Last edited by lindah (2011-06-01 17:59:10)

bobbym · 2011-06-01 17:53:15

I thought you would use:

for the second moment.

lindah · 2011-06-01 17:58:44

Sorry that was a typo, I did use

for the second part.
Am I on the right track at all?

bobbym · 2011-06-01 18:00:57

I think so, but help me out here. Your intervals of integration are from 0 to infinity, I have only seen a,b. Is this because you are working with a continuous distribution? Would a,b be for a discrete distribution?

You are correct for both moments!

lindah · 2011-06-01 18:18:27

This is how the function was originally defined so I am assuming it is like an exp function (continuous), I think the

you mention is actually ?

bobbym · 2011-06-01 18:24:16

Okay, now you have to set up 2 equations. I used:

What did you use instead of m1 and m2?

lindah · 2011-06-01 18:50:56

I used:

For

is where I get a bit confused as other examples e.g. normal and gamma distributions seem to incorporate .
I used:

Would this b correct?

After this I rearranged the first equation by taking the log of both sides, while for the second I rewrote it as:

and rearranged this in terms of

bobbym · 2011-06-01 19:54:03

Hi;

That is what I did also. Your work looks fine. I can not improve on it. If it is wrong, then we are both wrong.

lindah · 2011-06-01 20:09:50

Hi bobby,

Yes for the first and second moments, that is what I got exactly.

bobbym · 2011-06-01 20:24:44

Hi;

I think you were reading while I was editing so you saw the earlier post#10. I changed it to look like this.

Your work looks fine. I can not improve on it. If it is wrong, then we are both wrong.

lindah · 2011-06-01 21:13:39

Hi bobby,

Great, thanks for the assistance!! I'll remember to post the answer, when I get it

bobbym · 2011-06-01 21:16:25

Very good, glad to help.

lindah · 2011-06-24 13:34:45

lindah wrote:

Hi bobby,
Great, thanks for the assistance!! I'll remember to post the answer, when I get it

Looks like we got it wrong bobbym (I secretly blame you, jk) - used the wrong bounds

instead of

Similarly for

:

Calculating the variance:

Substituting this back gives:

bobbym · 2011-06-24 15:22:37

Hi lindah;

I blame that bobbym fellow. The guy is a moron, I can not figure how he ever gets a problem right.

A question of form:

It is usually written as

First integration is correct.

Second integration is correct.

Change the second integration to.

Now I just am not following your last statement...

gAr · 2011-06-24 17:54:08

Hi,

I used a moment generating function, got:

Is that what estimation of the parameters means?
edit: Yes, that is what it means!

Last edited by gAr (2011-06-24 23:55:52)

lindah · 2011-07-06 15:03:23

Hi gAr and bobby,

Apologies for delayed response, I've been on a little holiday.

Yes!!! That's the answer. Very interesting you used the mgf instead, its much more efficient!!!
Thank you for laying out an alternative

gAr · 2011-07-06 15:07:40

Hi lindah,

Okay, no problem. Hope you enjoyed your holidays.

You're welcome!

bobbym · 2011-07-06 15:45:02

Hi lindah;

I've been on a little holiday.

Okay, let me guess. You went to the Amazon. No, you visited the Nile delta. Oh wait, I got it, the Bimini wall. Or you climbed Everest, maybe you went to Vegas and put all that statistics to good use.

lindah · 2011-07-08 06:42:21

Hi bobbym,

I think I would be quickly escorted out of Vegas if I tried!
I actually went here for hiking http://www.parks.tas.gov.au/index.aspx?base=1253

bobbym · 2011-07-08 06:59:49

Hi;

Looks great. Did you do the entire 6 days?

lindah · 2011-07-13 15:09:40

Hi bobby,

Yes I did the full 6 days (I'm proud, it was torturous), but back in Sydney now - which is so cold atm.

bobbym · 2011-07-13 15:12:27

Hi lindah;

I got the impression from the reading that you are experiencing winter while it is summer here.

Also I had no idea you had to take so many precautions about not damaging the terrain.

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Parameter Estimation: Statistics

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