Robertson

Question 1

“Serious injuries”, 1993 NCCI definition

Answer 1

Fatal

Permanent Total

Major Permanent Partial

Question 2

Non-serious injuries, 1993 NCCI definition

Answer 2

Minor permanent partial

Temporary total

Medical only

Question 3

1993 NCCI hazard grouping

Answer 3

4 proposed hazard groups, linear combination of a few variables

Question 4

L¹ distance

Answer 4

Advantage: minimizes relative error in estimating excess premium

Question 5

L² distance

Answer 5

Euclidean distance; selected as analysis not sensitive to distance measure

Question 6

Why NCCI did not use standardization

Answer 6

Question 7

NCCI standardizing considerations

Answer 7

Question 8

Non-hierarchical clustering

Answer 8

New hazard groups did not have to be subsets of existing hazard groups

Question 9

k-means algorithm

Answer 9

1. Decide on number of clusters k to target
2. Start with initial arbitrary assignment into k clusters
3. Compute centroid (mean) of cluster
4. For each class, find closest centroid (L² distance) and assign to that cluster

If there has been any movement, repeat step 3

Question 10

Tests to determine number of hazard groups

Answer 10

Calinski and Harabasz

Cubic Clustering Criterion (CCC)

Question 11

Calinski and Harabasz statistic

Answer 11

“Pseudo-F test”

Higher values, better # of clusters

Question 12

Cubic Clustering Criterion

Answer 12

Compares amount of variance explained by a given set of clusters to that expected when clusters are formed at random; higher values better

Less reliable when data is highly correlated

Question 13

Why NCCI strayed from CCC

Answer 13

Question 14

“Crossover”

Answer 14

Counterintuitive results (i.e. exceptions to rules)

Question 15

Why NCCI went from 17 limits to 5 limits

Answer 15

ELFs at any pair of excess limits are highly correlated across classes

Limits below $100K were heavily represented

Wanted to cover range of limits commonly used for retro rating

Question 16

5 limits in NCCI study (2007)

Answer 16

$100K

$250K

$500K

$1M

$5M

Question 17

Credibility formula for NCCI Hazard Mapping

Answer 17

Z = min (1.5n / (n + k) , 1)

n = # of claims in the class

k = average # of claims per class

Question 18

Other credibility options in NCCI Hazard Group Mapping

Answer 18

1. Using median as k
2. Excluding Med-Only claims
3. Including only Serious claims
4. Requiring minimum # of claims for classes used to calculate k
5. Various square root rules

Question 19

UW feedback on proposed hazard grouping

Answer 19

Similarity between class codes in different hazard groups

Degree of exposure to auto accidents in a given class

Extent heavy machinery is used in a given class

Question 20

3 key ideas of remapping hazard groups

Answer 20

1. Computing excess ratios by class
2. Sorting classes based on excess ratios
3. Cluster analysis