A5. Robertson

Question 1

NCCI credibility weighted XS ratios

Answer 1

Rc Final = ZRc + (1-Z) Rhg
Z = min(n/(n+K) *1.5, 1)
where n = $ of claims in the class, k= average number of claims per class
Other credibility options:
- using median instead of vag of k
- exclude med only from n and k
- include only serious clains in n and k
- requiring min # of claims for classes used
- various square root rules

Question 2

Why did the NCCI use only 5 limits

Answer 2

1. XS ratios at any pair of limits are highly correlated across classes
2. Limits < $100K were heavily represented in the 17 prior limits
3. Using 1 limit would not have captured the full variability in XS ratios
4. These 5 limits are commonly used for rating

Question 3

Advantage of L1 distance

Answer 3

1. Minimize the relative error in estimating excess premium
2. Many small errors would have the same effect as one large error which results in outliers having less of an impact on the results

Question 4

Advantage of L2 distance

Answer 4

1. Penalizes large errors
2. minimize squared error

Question 5

What’s the goal of k-means clustering

Answer 5

minimize the variance within the K clusters and maximize variance between the k clusters

Question 6

differences between hierarchical vs. non-hierarchical

Answer 6

Hierarchical analyses subdivides a cluster into two clusters.
Non hierarchical seek the best partition of clusters for a pre-specified amount of clusters

Question 7

Total variance formula

Answer 7

summation of (Wc * (Rc - overall R )^2) / summation of (Wc)

Question 8

Within variance formula

Answer 8

summation of (Wc * (Rc - avg R for HGi)^2) / summation of (Wc)

Question 9

Between variance formula

Answer 9

summation of (Wc * (avg R for HGi - overall R)^2) / summation of (Wc)

Question 10

2 statistics used by NCCI to decide on # of proposed HGs

Answer 10

1. Calinski and Harabasz Statistics (C-H)
   = [trace(B)/ (k-1)] / [(trace(W)/(n-k)]
   = corrected between variance / corrected within variance
2. Cubic Clustering Criterion (CCC) statistics
   - compare the amount of variance explained by a given set of clusters to that expected when clusters are formed at random based on the multi-dimensional uniform distribution
   - less reliable when data is highly correlated
   For both methods, higher values indicate a better # of clusters