is random sample from negative binomial distribution .
I need to find moment estimators and .
My literature on this topic is very poor, any hints?
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?
NBI'd check the theoretical moments are correct if you aren't getting sensible answers. wikipedia is sometimes wrong about those