Robertson Flashcards
“Serious injuries”, 1993 NCCI definition
Fatal
Permanent Total
Major Permanent Partial
Non-serious injuries, 1993 NCCI definition
Minor permanent partial
Temporary total
Medical only
1993 NCCI hazard grouping
4 proposed hazard groups, linear combination of a few variables
L1 distance
Advantage: minimizes relative error in estimating excess premium
L2 distance
Euclidean distance; selected as analysis not sensitive to distance measure
Why NCCI did not use standardization
NCCI standardizing considerations
Non-hierarchical clustering
New hazard groups did not have to be subsets of existing hazard groups
k-means algorithm
- Decide on number of clusters k to target
- Start with initial arbitrary assignment into k clusters
- Compute centroid (mean) of cluster
- For each class, find closest centroid (L2 distance) and assign to that cluster
If there has been any movement, repeat step 3
Tests to determine number of hazard groups
Calinski and Harabasz
Cubic Clustering Criterion (CCC)
Calinski and Harabasz statistic
“Pseudo-F test”
Higher values, better # of clusters
Cubic Clustering Criterion
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
Why NCCI strayed from CCC
“Crossover”
Counterintuitive results (i.e. exceptions to rules)
Why NCCI went from 17 limits to 5 limits
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
