is random sample from negative binomial distribution .

I need to find moment estimators and .

My literature on this topic is very poor, any hints?

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- June 19th 2010, 07:51 AMlosm1Negative binomial moment estimators
is random sample from negative binomial distribution .

I need to find moment estimators and .

My literature on this topic is very poor, any hints? - June 19th 2010, 07:58 AMSpringFan25
My notation:

the sample mean:

the sample variance:

the population mean:

the population variance:

i assume you are trying to do a**method of moments**estimate of the parameters.

background info: http://en.wikipedia.org/wiki/Method_...ts_(statistics)

**Quick explanation**: equate the sample moments with the theoretical population moments

According to Negative binomial distribution - Wikipedia, the free encyclopedia, the moments for this distribution are:

So

To obtain the method of moments estimator, replace all the moments in the above equation with their sample analogues.

So your method of moment estimate for r is

Can you use a similar approach to find the estimate for p?

**NB**I'd check the theoretical moments are correct if you aren't getting sensible answers. wikipedia is sometimes wrong about those - June 19th 2010, 11:03 AMlosm1
I have checked NB formulas and used the right ones, is this ok?

- June 20th 2010, 02:11 AMSpringFan25
i hate wikipedia sometimes...

Your answer is perfect though :)