Revision as of 22:58, 13 May 2023 by Admin (Created page with "The distribution of accidents for 84 randomly selected policies is as follows: {| class = "table table-bordered" | Number of Accidents | Number of Policies |- | 0 | 32 |-...")
May 13'23
Exercise
The distribution of accidents for 84 randomly selected policies is as follows:
| Number of Accidents | Number of Policies |
| 0 | 32 |
| 1 | 26 |
| 2 | 12 |
| 3 | 7 |
| 4 | 4 |
| 5 | 2 |
| 6 | 1 |
| Total | 84 |
Determine which of the following models best represents these data.
- Negative binomial
- Discrete uniform
- Poisson
- Binomial
- Zero-modified Poisson
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
May 14'23
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.