I wonder how to distinguish between 2 types of negative binomial distribution. In the mock exam, question 8 states, that the number of claims follow a negative binomial distribution with k and p defined. How am I supposed to know to use type II instead of type I if the question does not provide enough info to determine the choice?
You should assume type 2 as the default for CT6. However, the key is in the values it can take. Type 2 takes values 0, 1, 2, ... which makes it suitable for the number of claims. Type 1 takes values k, k+1, k+2, ... where k is a positive integer. So if k=1 then claims would be 1, 2, 3, ... so this would mean you all policies make at least one claim - which is clearly suspect!
