Exercise
May 14'23
Answer
Key: A
[[math]]\begin{array}{cc}k & k n_{k} / n_{k-1} \\ 0 & \\ 1 & 0.81 \\ 2 & 0.92 \\ 3 & 1.75 \\ 4 & 2.29 \\ 5 & 2.50 \\ 6 & 3.00\end{array}[[/math]]
Positive slope implies that the negative binomial distribution is a good choice. Alternatively, the sample mean and variance are 1.2262 and 1.9131 respectively. With the variance substantially exceeding the mean, the negative binomial model is again supported.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.