A.03.Robertson

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  1. Hazard group
    Collection of workers compensation classifications that have relatively similar expected XS loss factor over a broad range of limits
  2. 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
  3. 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))
  4. 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
  5. 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
  6. 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
  7. Euclidian distance btwn vectors (L2)
    Image Upload
  8. 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
  9. 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)
  10. 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
  11. 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

Card Set Information

Author:
Exam8
ID:
162734
Filename:
A.03.Robertson
Updated:
2012-08-14 01:35:36
Tags:
NCCI hazard group excess ratio cluster
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Description:
NCCI's 2007 Hazard Group Mapping
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