Differences between Type I and Type II Negative Binomial Distribution and how to identify which is it?
Type 1 counts the number of trials up to and including the kth success.
Type 2 counts the failures before the kth success.
So suppose we are counting the number of goals we score (success) for the penalty kicks we make (trials).
Suppose we score our 3rd goal on our 10th penalty kick.
Under Type 1 X=10 as it is the 10th kick when we got our 3rd goal.
Under Type 2 X=7 as we had 7 failures before we got our 3rd goal.
In CT3 our default choice will be a type 1 (for CT6 it will be type 2).
Source -Nick Campbell
Suppose you've 9(n+1)4^(-n-2) how can you show that it is type 2 negative binomial distribution
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