CAS Exam 8 Fall 2017, Question 2
Study guide: Exam 8
An actuary wants to cluster five Workers' Compensation classes based on excess ratios at two limits: 500,000 and 1,000,000. The actuary decides to use a weighted k-means algorithm with two clusters. Given the following:
| Class | On-Leveled Earned Premium ($ Thousands) | Normalized Excess Ratio at 500,000 Limit | Normalized Excess Ratio at 1,000,000 Limit | Initial Cluster |
|---|---|---|---|---|
| 1 | 6,500 | 0.240 | 0.080 | A |
| 2 | 5,000 | 0.350 | 0.200 | A |
| 3 | 4,000 | 0.210 | 0.080 | A |
| 4 | 3,000 | 0.110 | 0.030 | A |
| 5 | 5,000 | 0.180 | 0.070 | B |
- Distance will be measured using the
L^2(Euclidean) norm. - At the start of the algorithm, the actuary randomly assigns each class to a cluster.
Part a (1.75 points)
Determine the cluster for each class after the first iteration of the weighted k-means algorithm.
Part b (0.25 points)
Briefly describe one advantage of using the L^1 measure rather than L^2 when computing clusters.
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