A.03.Robertson

Collection of workers compensation classifications that have relatively similar expected XS loss factor over a broad range of limits

• 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

• based on class ELF & cluster analysis
• ELF vary by state, but not hazard group
• R_j(L) = Σ w_i,j s_i (L / μ_i,j)
• w_i,j = % loss due to injury type i
• S_i = state normlized xs ratio function
• L / μ_i,j = entry ratio point
• XS ratio vector = R_C = (R_C(L₁), ..., R_C(L_n))

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

• z = min(n / n+ k * 1.5, 1), k = mean clm cnt
• 1 - z given to R_HG (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

• 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

• 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 i^th group
•  |HG_i| = # of classes in hazard group i

• 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)

• 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

• XS ratios were credibility weighted w prior HG
• low cred classes have similar vectors → end up together