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Hazard group
Collection of workers compensation classifications that have relatively similar expected XS loss factor over a broad range of limits
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1993 NCCI review
- used principal components analysis on 3 yrs
- serious clm freq / total clm frq by class / statewide
- serious clm indemnity severity by class / statewide
- serious PP by class / statewide
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2007 NCCI review
- based on class ELF & cluster analysis
- ELF vary by state, but not hazard group
- Rj(L) = Σ wi,j si (L / μi,j)
- wi,j = % loss due to injury type i
- Si = state normlized xs ratio function
- L / μi,j = entry ratio point
- XS ratio vector = RC = (RC(L1), ..., RC(Ln))
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Corro & Engl
A distribution is characterized by its excess ratios and so there is no loss of information in working with xs ratios rather than w size of loss
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Robertson hazard group credibility
- z = min(n / n+ k * 1.5, 1), k = mean clm cnt
- 1 - z given to RHG (previous hazard group)
- k - using median: too low, z too high
- exl medical only
- incl only serious claims
- k = mean of all classes w some minimum threshould → rejected, k was too high
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Building hazard groups - Limits
- how to choose n and actual limits
- correlation btwn neighboring XS ratios is high
- looked at more limits, but they weren't gaining much info due to strong correlation for closer limits
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Euclidian distance btwn vectors (L2)
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Cluster method
- if 2 objects are in diff clusters in the k cluster partition, then they will be in different clusters in all partitions w more than k elements
- k-mean: for k clusters, group classes into k groups as to minimize the euclidian distance between elements
- centroid: avg xs ratio vector for ith group
- |HGi| = # of classes in hazard group i
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Optimal # of clusters
- Calinski & Harabasz statistic = [trace(B) / (k -1) / [trace(W)] / (n - k)]
- n = # of classes, k = # of clusters
- maximize it (high means higher btwn & lower within)
- Cubic Clustering Criterion (CCC): compares amt of variance explained by a given set of clusters to rdm clusters
- (-) less reliable when data is elongated (variables are highly correlated)
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Reasons why NCCI kept 7 hazard groups
- Calinksi & Harabasz gave right answer more time than CCC on control data
- CCC less reliable when var are highly correlated
- both test indicated 7 when only class w high cred were used
- 9 HG sln produces crossovers
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NCCI update - why B & E have many classes
- XS ratios were credibility weighted w prior HG
- low cred classes have similar vectors → end up together
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