7.7 Method 6) Distribution Model

Use a modeled severity distribution (e.g. Weibull) for each age

• Parameters vary @ different ages; make sure they are consistent

  e.g. Parameters for Weibull, \((\theta, \omega)_t\), are different depending on age

• \(R^L_t = \dfrac{\mu^L_t}{\mu_t}\)

  • Mean of Weibull: \(\mu^L_t = \theta \cdot \Gamma \left(1 + \frac{1}{\omega}\right)\)

Advantages

• Maintain the relationships of the limited and unlimited over time

• Can easily interpolate among limits and years

Then we can use the distribution and then applies all the relationships discussed in Method 5