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Extended link ratio family
- Assumes heteroscedastic normality
- Standard link ratio model carry assumptions not usually satisfied by data
- E(y|x) = bx
- Diagnostic test - wtd stadardized residuals vs fitted value should appear rdm
- Downward trend indicated that large values are overpredicted and small values are underpredicted
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Statistical modeling framework
- Possibility of parameters in:
- Acc yr - determines level from yr to yr
- Dvpmt yr - orthogonal to acc yr
- Pmt yr - trend from pay yr to pay yr
median = exp(α + Σγk) - mean = median * exp(0.5σ²)
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Statistical Modeling: Assumptions about future
- If pmt / CY trend has been stable in the more recent yrs, assumptin relatively straightforward
- If unstable, assumptions about future will depend on explanation for the instability
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Statistical Modeling: prediction intervals
- In an insr writes more than one long-tail line and aims for a 100(1 - α)% security level on all the lines combined, then the risk margin per line decreases the more lines the company writes.
- Let se = standard error and rm = risk margin:
- se(Total) = √[se²(1) + ... + se²(n)]
- if rm(all lines) = k*se(Total) thenrm(j) = k*se(j)/Σse(i) < k*se(j)
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