Continuing with the example of a $20 million loss whose frequency is once in 10 years, in order to merge this scenario with internal loss data from 5 years' experience, we will have to consistently recreate internal data with a sample size equivalent to a period of 10 years.
From preliminary research, we have undertaken on external data, we are not comfortable using our approach on units of measure that have insufficient internal loss data to develop a meaningful and stable model.
This choice is consistent with the continuous distributions we use for modeling the severity of internal loss data.
i] is the number of losses observed annually, sampled from the frequency distribution of the internal loss data for that particular unit of measure.
Assumption 1: During a short and reasonably specified period of time, such as 1 year or less, the frequency and severity distributions based on the internal loss data for a unit of measure do not change.
Our analysis does not use scenario data as a substitute for internal loss data.
In our experiments, however, probabilities based on internal loss data have proved to be much more stable than those based on both internal and external loss data.
Discussion of the choice and appropriateness of a distribution for fitting the internal loss data is beyond the scope of this work.
Table 1 shows the results of goodness-of-fit tests for five distributions used to model the internal loss data for a particular unit of measure at a financial institution.
Any of the five distributions could be used to model the internal loss data.
In that sense, loglogistic has the best predictive power for the given set of scenarios, conditional on the internal loss data.