I have a sequence of iid negative binomial random variables with a known p parameter but unknown r parameter. In other words we know what the probability of success of a given trial is, but we do not know how many successes are needed to stop the experiment. The pdf of the distribution is:
$f(x)$=$x_i-1\choose r-1$ $p^r$$(1-p)^{x_i-r}$ for $x_i\geq r$.
I am unsure how exactly to perform the MLE estimation procedure for this function when searching for an estimator of r. Could anyone help me out?