I'm working through an old qualifying exam and I feel like I'm so close to the answer. Given a random sample of size n from a negative binomial distribution with parameters (r,p) I need to find a UMVU estimator for p/(1-p). The mean of a negative binomial is r(1-p)/p so the UMVU estimator for this would just be the sample mean over r since the sample mean is a complete and sufficient statistic. When the problem is inverted though you can't use the linearity of expectations to sum the means so I'm a bit lost.
2026-02-24 01:33:49.1771896829
Uniformly minimum variance unbiased estimator for negative binomial distribution
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