Which of the following statements is true:

Which of the following statements is true:

I. When averaging quantiles of two Pareto distributions, the quantiles of the averaged models are equal to the geometric average of the quantiles of the original models based upon the number of data items in each original model.

II. When modeling severity distributions, we can only use distributions which have fewer parameters than the number of datapoints we are modeling from.

III. If an internal loss data based model covers the same risks as a scenario based model, they can can be combined using the weighted average of their parameters.

IV If an internal loss model and a scenario based model address different risks, the models can be combined by taking their sums.
A . II and III
B . III and IV
C . I and II
D . All statements are true

View Answer

Answer: D

Explanation:

Statement I is true, the quantiles of the averaged models are equal to the geometric average of the quantiles of the original models.

Statement II is correct, the number of data points from which model parameters are estimated must be greater than the number of parameters. So if a distribution, say Poisson, has one parameter, we need at least two data points to estimate the parameter. Other complex distributions may have multiple parameters for shape, scale and other things, and the minimum number of observations required will be greater than the number of parameters.

Statement III is true, if the ILD data and scenarios cover the same risk, they are essentially different perspectives on the same risk, and therefore should be combined as weighted averages.

But if they cover completely different risks, the models will need to be added together, not averaged – which is why Statement IV is true.