Hi, I understand that Type2 Negative Binomial gives X as the number of failure before the kth success. How can this distribution be used to model no. of claims? From the solution, k is given as 1.8569. What is the relationship between k and the number of claims in a policy?
That's how we can construct the formula from a real life situation for integer k. However, the distribution can be generalised beyond this situation - to a discrete random variable taking values 0, 1, 2, .... whereupon it loses it's real life meaning. So unfortunately there is not a clear connection. It's just a discrete distribution that can be used to model claim numbers as it takes values 0, 1, 2, ... (like the Poisson). However it is a good alternative to the Poisson as it doesn't have equal mean and variance. Sorry it's not the answer you'd like!
