CAS Exam 8 Fall 2019, Question 4
Study guide: Exam 8
An actuary wants to cluster six workers compensation classes based on excess ratios at two limits: 750,000 and 1,500,000. The actuary decides to use a weighted k-means algorithm with three clusters. Given the following:
| Class | On-Leveled Earned Premium | Normalized Excess Ratio at 750,000 Limit | Normalized Excess Ratio at 1,500,000 Limit | Initial Cluster |
|---|---|---|---|---|
| 1 | 7,000,000 | 0.250 | 0.095 | A |
| 2 | 8,000,000 | 0.200 | 0.080 | B |
| 3 | 7,500,000 | 0.170 | 0.062 | C |
| 4 | 6,000,000 | 0.130 | 0.048 | A |
| 5 | 5,000,000 | 0.450 | 0.217 | A |
| 6 | 8,500,000 | 0.240 | 0.098 | B |
- At the start of the algorithm, the actuary randomly assigned each class to a cluster.
- The actuary has observed that the 750,000 limit is selected by the insured 75% of the time, consistent across all six classes.
Briefly justify which measure to use to calculate the distance between vectors and using that measure, determine the cluster for each class after the first iteration of the weighted k-means algorithm.
Part a (3 points)
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